DE102023129996A1 - ML-BASED SECURITY PROOF OF QUANTUM COMMUNICATION PROTOCOLS WITH NOISY QUANTUM CHANNELS - Google Patents

Abstract

Disclosed is a method for sharing information using a data exchange system comprising a sender node and a receiver node using a noisy quantum channel in accordance with a quantum communication protocol, the method comprising: providing a trained machine learning model, the machine learning model configured to receive a noise model of noise of a noisy quantum channel of a given system and a set of parameters of the given system to predict whether the given system is safe or unsafe for sharing information according to the quantum communication protocol, the set of parameters indicating a degree of success of a third-party attack and a degree of reception success at the receiver node of the given system and describing the given system; determining a noise model for noise of the noisy quantum channel of the data exchange system; evaluating the set of parameters for the data exchange system for sharing the information; Inputting the evaluated set of parameters and the noise model into the machine learning model, thereby obtaining a prediction of the security of the data exchange system; aborting the quantum communication protocol if the data exchange system is determined to be insecure.

Description

FIELD OF THE INVENTION

The invention relates to the field of data communication and, more particularly, to a method for sharing information between nodes using a noisy quantum channel according to a quantum communication protocol.

BACKGROUND

Quantum communication is a field that exploits the quantum mechanical properties of a quantum system, properties such as superposition and entanglement, to enable secure and efficient communication protocols. It offers a wide range of applications, such as quantum key distribution (QKD), which allows two parties to securely exchange cryptographic keys. Any attempt to intercept the quantum signal by a third party can disrupt the quantum state and alert legitimate users. Another important application of quantum communication is quantum teleportation and quantum cryptography. However, there is a need for improved use of QKD.

SUMMARY

The aim of the invention is to provide a method for sharing information using a data exchange system comprising a sender node and a receiver node and using a noisy quantum channel in accordance with a quantum communication protocol. The objects underlying the invention are achieved by the features of the independent claims.

Embodiments provide a method for sharing information using a data exchange system comprising a sender node and a receiver node using a noisy quantum channel in accordance with a quantum communication protocol, the method comprising: providing a trained machine learning model, wherein the machine learning model is configured to receive a noise model of noise of a noisy quantum channel of a given system and a set of parameters of the given system to predict whether the given system is safe or unsafe for sharing information according to the quantum communication protocol, wherein the set of parameters indicates a degree of success of a third-party attack and a degree of reception success at the receiver node of the given system and describes the given system; determining a noise model for noise of the noisy quantum channel of the data exchange system; evaluating the set of parameters for the data exchange system for sharing the information; Inputting the evaluated set of parameters and the noise model into the machine learning model, thereby obtaining a prediction of the security of the data exchange system; aborting the quantum communication protocol if the data exchange system is determined to be insecure.

Embodiments provide a computer program containing instructions for causing a computer system to perform the method of the above embodiment.

Embodiments provide a computer system for controlling a data exchange system comprising a sender node and a receiver node, the data exchange system configured for sharing information using a noisy quantum channel in accordance with a quantum communication protocol, the computer system configured to: provide a trained machine learning model, the machine learning model configured to receive a noise model of noise of a noisy quantum channel of a given system and a set of parameters of the given system to predict whether the given system is safe or unsafe for sharing information according to the quantum communication protocol, the set of parameters indicating a degree of success of a third-party attack and a degree of reception success at the receiver node of the given system and describing the given system; determine a noise model for noise of the noisy quantum channel of the data exchange system; evaluate the set of parameters for the data exchange system for sharing the information; Inputting the evaluated set of parameters and the noise model into the machine learning model, thereby obtaining a prediction of the security of the data exchange system; aborting the quantum communication protocol if the data exchange system is determined to be insecure.

It is understood that one or more of the aforementioned embodiments may be combined, as long as the combined embodiments do not exclude each other.

BRIEF DESCRIPTION OF THE DRAWINGS

• ein Blockdiagramm eines Systems ist, welches einem Beispiel des vorliegenden Gegenstands entspricht.
• 2 ein Diagramm ist, das ein maschinelles Lernmodell gemäß einem Beispiel des vorliegenden Gegenstands illustriert.
• 3 ein Flussdiagramm eines Verfahrens zum Teilen von Informationen zwischen einem Senderknoten und einem Empfängerknoten in Übereinstimmung mit einem Quantenkommunikationsprotokoll ist.
• 4 ein Flussdiagramm eines Sicherheitsnachweisverfahrens in Übereinstimmung mit dem Quantenkommunikationsprotokoll ist.
• 5A ein Diagramm ist, das ein Beispiel eines Quantenkommunikationssystems gemäß einem Beispiel des vorliegenden Gegenstands darstellt.
• schematisch ein Beispiel eines Quantenschaltungssystems für das Drittpartei-Quantencomputersystem gemäß einem Beispiel des vorliegenden Gegenstands zeigt.
• schematisch ein Beispiel eines Quantenschaltungssystems für das Drittpartei-Quantencomputersystem gemäß einem Beispiel des vorliegenden Gegenstands zeigt.
• schematisch ein Beispiel eines Quantenschaltungssystems für das Drittpartei-Quantencomputersystem gemäß einem Beispiel des vorliegenden Gegenstands zeigt.
• 6A ein Diagramm ist, das ein Beispiel eines Quantenkommunikationssystems gemäß einem Beispiel des vorliegenden Gegenstands darstellt.
• 6B schematisch ein Beispiel eines Quantenschaltungssystems für das Drittpartei-Quantencomputersystem gemäß einem Beispiel des vorliegenden Gegenstands zeigt.
• 7 ein Flussdiagramm eines Verfahrens zur Optimierung der Parameter eines Quantenschaltungssystems gemäß einem Beispiel des vorliegenden Gegenstands ist.

Examples are described in more detail below with reference to the drawings in which:

• is a block diagram of a system corresponding to an example of the present subject matter.
• 2 is a diagram illustrating a machine learning model according to an example of the present subject matter.
• 3 is a flowchart of a method for sharing information between a sender node and a receiver node in accordance with a quantum communication protocol.
• 4 is a flowchart of a security proof procedure in accordance with the quantum communication protocol.
• 5A is a diagram illustrating an example of a quantum communication system according to an example of the present subject matter.
• schematically shows an example of a quantum circuit system for the third-party quantum computing system according to an example of the present subject matter.
• schematically shows an example of a quantum circuit system for the third-party quantum computing system according to an example of the present subject matter.
• schematically shows an example of a quantum circuit system for the third-party quantum computing system according to an example of the present subject matter.
• 6A is a diagram illustrating an example of a quantum communication system according to an example of the present subject matter.
• 6B schematically shows an example of a quantum circuit system for the third-party quantum computing system according to an example of the present subject matter.
• 7 is a flowchart of a method for optimizing the parameters of a quantum circuit system according to an example of the present subject matter.

DETAILED DESCRIPTION

In the following, similar elements are designated with the same numbers.

The present subject matter may enable two or more remote parties to communicate securely with each other. In particular, the present subject matter may enable an accurate assessment of the security level of communication over the noisy quantum channels.

Quantum computers can enable secure access to information. Quantum channels can be used for this purpose. A quantum channel can be a communication channel capable of transmitting quantum information. A quantum channel can also be used to transmit classical information. An example of quantum information can be information that specifies the state of a qubit. The state of a qubit can refer to the state of the computational basis of a particular basis/the computational basis state of a particular basis. A qubit can be physically realized by a quantum system with two states, where the quantum system can be, for example, a photon or an ion. The quantum channel can be realized, for example, by optical fibers or free space. For example, the vertical and horizontal polarization of a photon can be used as a qubit state. The two energy levels of an ion can be used as a qubit state. For a qubit represented by a photon, the computational basis states can be, for example, horizontal and vertical polarization states or diagonal and antidiagonal polarization states.

The quantum channel can be used to share or deliver information. For example, a system (called a data exchange system or quantum communication system) with transmitter nodes and receiver nodes is envisioned. The transmitter node can, for example, comprise a transmitter quantum computer system, and the receiver node a receiver quantum computer system. The terms "receiver node" and "receiver quantum computer system" are used interchangeably. The terms "transmitter node" and "transmitter quantum computer system" are used interchangeably. The data exchange system can comprise the transmitter quantum computer system connected to the receiver quantum computer system via the quantum channel. The quantum channel can be subject to one or more types of noise. The quantum channel can therefore also be referred to as a noisy quantum channel. The noise of the noisy quantum channel can refer to the noise to which the noisy quantum channel is subject. The noise can cause errors, decoherence, and other forms of degradation of the transmitted quantum information. The amplitude-damping noise can be caused, for example, by Interactions with the noisy environment arise, e.g., due to thermal fluctuations or other sources of energy dissipation. Amplitude-damping noise can affect the amplitude of a quantum state, causing it to decrease over time, leading to errors in the transmitted information. In another example, phase-damping noise can arise from interactions with the environment, e.g., due to fluctuations in the phase of the quantum system or other sources of phase decoherence. Phase-damping noise can be a form of decoherence that affects the phase of a quantum state, causing it to decrease over time, leading to errors in the transmitted information. The data exchange system can be described by system parameters such as the distance between the transmitter node and the receiver node, the detector efficiency of a signal detector at the receiver node, and the design parameters of the data exchange system components. The system parameters may further specify the amount of information shared between the sender node and the receiver node. In one example, the system parameters may also include the quantum bit error ratio (QBER). The data exchange system may be a real system (i.e., not a simulated system) used for real-world information sharing over the noisy quantum channel.

For example, the sender quantum computer system can use the noisy quantum channel to share information with the receiver quantum computer system, or vice versa. The shared information can, for example, be encoded in qubit states that travel through the noisy quantum channel from the sender quantum computer system to the receiver quantum computer system.

The sharing of information between the sender quantum computer system and the receiver quantum computer system may occur in accordance with the quantum communication protocol. The quantum communication protocol may be a system of rules that allows two or more entities of a communication system to share (e.g., transmit) information. The quantum communication protocol may, for example, define the rules, syntax, semantics, and synchronization of the communication, as well as possible error recovery procedures. In one example, the quantum communication protocol may be used by the sender quantum computer system and the receiver quantum computer system to obtain two identical copies of a bit sequence, where the shared information may include at least the bit sequence. The bit sequence may, for example, be random and secret. The sender quantum computer system may, for example, prepare qubits in states that each represent the bit sequence. The quantum communication protocol may, for example, be a single-qubit-based protocol or an entangled-state-based protocol.

The present subject matter may enable two or more remote parties to communicate securely with each other. In particular, the present subject matter may enable an accurate assessment of the security level of communication over the noisy quantum channel, taking into account errors that may be caused both by the noise of the noisy quantum channel and by eavesdropping. For this purpose, a third-party quantum computing system (also referred to as a third party) may be provided. The third-party quantum computing system may be configured to connect to the noisy quantum channel between the sender quantum computing system and the receiver quantum computing system. The sender quantum computing system may prepare qubits in corresponding basis states and send them to the receiver quantum computing system over the noisy quantum channel. The receiver quantum computing system may be configured to receive the prepared qubits over the noisy quantum channel and measure their states. The third-party quantum computing system may be configured to intercept the prepared qubits on the noisy quantum channel and determine or estimate their states, and send the intercepted qubits to the receiving node via the noisy quantum channel. In one example, the third-party quantum computing system may be configured to intercept the prepared qubits on the noisy quantum channel and determine their states without destroying or altering the states of the intercepted qubits, and send the qubits to the receiving node via the noisy quantum channel. In one example, the third-party quantum computing system may be configured to intercept the prepared qubits on the quantum channel, create approximate copies of the intercepted qubits, send the approximate copies to the receiving node via the noisy quantum channel, and use the approximate copy of the intercepted qubit to estimate the state of the intercepted qubit. The third-party quantum computing system may enable the simulation of attacks or eavesdropping on the noisy quantum channel. The third-party quantum computing system may be used to evaluate the degree of success of an attack (i.e., the degree of success of eavesdropping on the noisy quantum channel). For example, the third-party quantum computing system may used to evaluate a first metric representing the degree of success of an attack. The first metric may, for example, be a distance measure such as fidelity. For example, the third-party quantum computing system may be used to determine elements of the density matrices that can be used to calculate the fidelity between the state of the intercepted qubit and a state of the prepared qubit as prepared by the sender node. Each quantum computing system of the sender quantum computing system, the receiver quantum computing system, and the third-party quantum computing system may, for example, comprise a quantum circuit system. The quantum circuit system may utilize the principles of quantum mechanics to perform quantum computations through the operation of one or more qubits. The quantum circuit system may further utilize the principles of quantum mechanics to perform quantum communication, e.g., to send or receive quantum information. The quantum circuit system may, for example, be a quantum computer. For example, each quantum computer system may be a photonic quantum computer that uses photons to represent qubits, where the quantum circuit system may, for example, include components such as a polarization controller, a pulse pattern generator, a light source, a planar lightwave circuit, or any other component that enables the quantum circuit system to perform quantum computations and/or quantum communication. The respective quantum computer system may, for example, be configured to perform classical computations using a classical computer or by simulating classical computations. The classical computer may, but need not, be part of the respective quantum computer system. The classical computer may include the hardware, such as a processor and memory, and software, such as an operating system. The receiving quantum computer system may be used to evaluate reception success. For example, the receiving quantum computer system may be used to evaluate a second metric indicating the degree of reception success. The second metric may, for example, be a distance measure such as fidelity. For example, the receiver quantum computer system can be used to determine elements of the density matrices that can be used to calculate the fidelity between the state of the received qubit and a state of the prepared qubit as prepared by the sender node.

The third-party quantum computing system may be configured to provide a third-party quantum system. The third-party quantum system may be defined according to an attack configuration of a simulated attack. For example, the third-party quantum system may be defined by the prepared qubit intercepted on the noisy quantum channel and a set of one or more additional qubits. For example, the third-party quantum computing system may comprise the quantum circuit system containing the intercepted qubit and the set of additional qubits. The quantum circuit system may be further configured to perform a set of one or more quantum operations with specific parameters. The quantum operation may be a unitary operation. Applying the set of one or more quantum operations can make it possible to determine or predict the state of the intercepted qubit (without destroying its state) by measuring one or more additional qubits of the quantum circuit system after applying the set of one or more quantum operations. After applying the set of one or more quantum operations, the intercepted qubit can remain unchanged and be sent back from the quantum circuit system to the receiving node via the noisy quantum channel. The quantum operation can, for example, be an operation or a sequence of operations of a particular set of universal quantum gates, including, for example, the rotation operators and the controlled not-not (CNOT) operator.

For example, the set of one or more quantum operations may be a controlled operation using the intercepted qubit as a control qubit. The controlled operation may, for example, be a controlled rotation applied to the additional qubit, using the intercepted qubit as a control qubit. The controlled operation may, for example, be a CNOT operation acting on two qubits to perform the NOT operation on the additional qubit based on the state of the intercepted qubit. After applying the controlled operation, the intercepted qubit may remain unchanged and be sent back from the quantum circuit system to the receiver node via the noisy quantum channel. After applying the controlled operation, the state of the additional qubit involved in the controlled operation may indicate the state of the intercepted qubit. In another example, the set of quantum operations may include the controlled operation in addition to further quantum operations. The additional quantum operations may be applied to at least one Part of the set of additional qubits can be applied. After applying the set of quantum operations, at least one of the set of additional qubits can be measured, and the result of the measurement can be used to determine or estimate the state of the intercepted qubit.

For example, the third-party quantum computing system may comprise control means that control the states of the qubits of the quantum circuit system, e.g., control the quantum circuit system to perform the set of quantum operations. The quantum operation may be applied to at least a portion of the qubits of the quantum circuit system. The quantum operation may be a controlled quantum operation, with the intercepted qubit serving as a control for the quantum operation. The specific parameters of the quantum circuit system may, for example, be parameters of the quantum operations, such as rotation angles of rotation operations. For example, the state of the qubit may be transformed by rotation around the x, y, and z axes in the Bloch sphere.

However, the noise acting on the qubits can lead to decoherence, and the qubits received at the receiving node may not exactly match what would be expected without noise. Therefore, one must deal with the interference caused by eavesdropping and the noise of the noisy quantum channel. A machine learning (ML) model can be used for this purpose. The noise of the noisy quantum channel of the data exchange system can be described by a noise model. The noise model specifies at least one of the following characteristics: depolarizing channel noise, amplitude-damping channel noise, phase-damping channel noise, or bit-flip channel noise. The type of noise of the noisy quantum channel of the data exchange system can be determined, for example, by a user of the data exchange system. Alternatively, the type of noise of the noisy quantum channel of the data exchange system can be determined, for example, from metadata describing the data exchange system.

For example, the machine learning model can be used to predict the security of shared information across a data exchange system (e.g., in real time). This refers to the inference phase of the machine learning model. The machine learning model can be defined as follows. The machine learning model is configured to receive as input the values of a set of parameters evaluated for a given system, where the given system includes a given receiver node and a given transmitter node configured to share information across a given noisy quantum channel connecting the given receiver node to the given transmitter node in accordance with the quantum communication protocol and a noise model of the noise of the given noisy quantum channel. Furthermore, the machine learning model can receive as input the noise model describing the noise of the given noisy quantum channel of the given system. For example, the noise model can be encoded using techniques such as one-hot encoding to convert it into a numerical format that machine learning algorithms can understand. In response to receiving the values of the set of parameters and the noise model, the machine learning model can provide an output, where the output indicates whether the given system is safe or unsafe for sharing information. For example, the machine learning model can be trained with different noise models so that the input noise model can be used by the trained machine learning model to predict the security of the data sharing system by applying what it has learned for that noise model.

The set of parameters input to the trained machine learning model (e.g., in the inference phase) includes the system parameters and the values of the first and second metrics of the data exchange system. For example, in addition to the system parameters of the data exchange system, the values of the first metric and the second metric, as well as the noise model, can be provided as input to the trained machine learning model. In response to the input (i.e., the values of the set of parameters and the noise model), the trained machine learning model can predict whether the data exchange system is secure or insecure. A data exchange system that is secure means that sharing the information (e.g., the bit sequence) is safe, and therefore the sharing will not be aborted. A data exchange system that is insecure means that sharing the information (e.g., the bit sequence) is unsafe and therefore aborted, so that the shared information cannot be used because a third party has access to it. In this way, the trained machine learning model can automatically detect abnormal combinations of the set of parameters and classify them into a secure or insecure system. This can create a universal model for detecting or preventing attacks by For example, a method for calculating forward propagation is used.

In one example, the system parameters may include a first subset of parameters describing the design (e.g., structure and components) of the data exchange system and a second subset describing the operation of the data exchange system. The second subset of parameters may include at least one of the following: the amount of information (e.g., the number of bits) shared by the data exchange system or the time at which the data exchange is performed by the data exchange system. The second subset of parameters may enable a customizable description of the data exchange system based on its operation. This may enable accurate classification of the data exchange system.

The termination of the quantum communication protocol can, for example, consist of transmitting a warning or error signal to the sender quantum computer system and the receiver quantum computer system. This signal can indicate that the communication is insecure and that the shared information can be viewed by an eavesdropper or listening device.

In one example, after receiving the warning signal, the sender quantum computer system and the receiver quantum computer system may share the information by adapting the quantum communication protocol, or repeat the sharing of the information at a different time, or abort the sharing of the information. In one example, in response to the aborting of the quantum communication protocol, the information may be shared again (e.g., at a later time) between the sender quantum computer system and the receiver quantum computer system, the set of parameters may be evaluated, and a further check may be performed against the trained ML model as to whether or not to abort the quantum communication protocol. This may be advantageous if the security issue is time-limited, e.g., if it only occurs due to temporal misconfigurations. In one example, in response to the aborting of the quantum communication protocol, the quantum communication protocol may be adapted, and the method may be repeated using the adapted quantum communication protocol.

For example, if the data exchange system is secure, the shared information can be considered secure and thus used by both the sender and receiver nodes. For example, if the system is considered secure, the quantum communication protocol cannot be aborted, but its execution can continue to share the information between the sender and receiver nodes.

$$

Auf diese Weise können die Auswirkungen des Rauschens auf die Qubits in Bezug auf die Fidelität der im Senderknoten vorbereiteten Qubits und der bei der dritten Partei erhaltenen Qubits verglichen werden, indem verschiedene verrauschte Quantenkanäle, die die Qubits durchlaufen, berücksichtigt werden. Im Falle des amplitudendämpfenden Rauschens kann das Rauschen beispielsweise durch Kraus-Operatoren charakterisiert werden, so dass die Entwicklung des Zustands des vorbereiteten Qubits durch Anwendung der Kraus-Operatoren modelliert werden kann.In one example, the first metric can be the fidelity between the state of the intercepted qubit, as determined or estimated by the third party, and a state of the prepared qubit, as prepared by the sender. The state of the prepared qubit can be represented by a density matrix ρ ₁ , and the state of the intercepted qubit can be represented by a density matrix ρ ₂ . The first metric can thus be defined as follows: $F_2\left({\mathrm{<figure-callout\; id="1"\; label="\rho "\; filenames="DE102023129996A1\_0019.png"\; state="\{\{state\}\}">\rho </figure-callout>}}_1,{\rho }_2\right)={\left(\text{<figure-callout id="1" label="tr ρ" filenames="DE102023129996A1\_0019.png" state="{{state}}">tr</figure-callout>}\sqrt{\sqrt{{\rho }_{}}}\sqrt{\sqrt{{}_1}{\rho }_2\sqrt{{\rho }_1}}\right)}^2.$

$$

In this way, the effects of noise on the qubits can be compared in terms of fidelity between the qubits prepared at the sender node and those received at the third party, by considering different noisy quantum channels through which the qubits pass. For example, in the case of amplitude-damping noise, the noise can be characterized by Kraus operators, allowing the evolution of the state of the prepared qubit to be modeled by applying Kraus operators.

wobei X die Zufallsvariable sein kann, die mit Bits im Sender-Quantencomputersystem verbunden ist, und Y die Zufallsvariable sein kann, die Bits im Quantensystem der dritten Partei zugeordnet ist, wobei p(x,y) die gemeinsame Wahrscheinlichkeit ist, und p(x) und p(y) die individuellen Wahrscheinlichkeiten sind.In one example, the quantum communication protocol can be used by the sender quantum computer system and the receiver quantum computer system to obtain two identical copies of a bit sequence, where the shared information can be the bit sequence. The bit sequence can be random and secret, for example. The third-party quantum computer system can attempt to learn the original bits. During this shared information process, each of the three parties can receive a bit sequence. The three strings can be interpreted as binary random variables. The degree of dependence between two random variables can be measured using the shared information. In one example, the first metric can alternatively include the shared information (transinformation) between binary random variables of the sender node and the third party. The first metric can be the shared information (transinformation) between binary random variables of the sender node and the third party. The shared information can be defined, for example, as follows: $I\left(X,Y\right)={\displaystyle \sum {}_x{\displaystyle \sum {}_{y}p\left(x,y\right){\text{log}}_2\left(\frac{p\left(x,y\right)}{p\left(x\right)p\left(y\right)}\right)}},$

where X can be the random variable associated with bits in the sen the quantum computer system, and Y can be the random variable associated with bits in the third party's quantum system, where p(x,y) is the joint probability, and p(x) and p(y) are the individual probabilities.

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Auf diese Weise können die Auswirkungen von Rauschen und Abhören auf Qubits in Bezug auf die Zuverlässigkeit der am Senderknoten vorbereiteten Qubits und der am Empfängerknoten erhaltenen Qubits verglichen werden, wobei verschiedene verrauschte Quantenkanäle, die die Qubits durchlaufen, berücksichtigt werden. Die Quelle Charles H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin. Experimental quantum cryptography. Journal of cryptology, 5:3-28 and Umesh Vazirani and Thomas Videck. Fully device-independent quantum key distribution. Physical Review Letters, 113(14), Sep 2014 bietet Beispielimplementierungen für die Auswertung der ersten Metrik und der zweiten Metrik.The second metric can be a fidelity between the state of the prepared qubit, as prepared by the sender node, and the measured state of the qubit received and measured by the receiver quantum computer system. The state of the prepared qubit can be represented by a density matrix ρ ₁ , and the state measured by the receiver quantum computer system can be represented by a density matrix ρ ₂ . The second metric can thus be defined as follows: $F_1\left({\mathrm{<figure-callout\; id="1"\; label="\rho "\; filenames="DE102023129996A1\_0019.png"\; state="\{\{state\}\}">\rho </figure-callout>}}_1,{\rho }_2\right)={\left(\text{<figure-callout id="1" label="tr ρ" filenames="DE102023129996A1\_0019.png" state="{{state}}">tr</figure-callout>}\sqrt{\sqrt{{\rho }_{}}}\sqrt{\sqrt{{}_1}{\rho }_2\sqrt{{\rho }_1}}\right)}^2.$

$$

In this way, the effects of noise and eavesdropping on qubits can be compared in terms of the reliability of the qubits prepared at the sender node and the qubits received at the receiver node, taking into account different noisy quantum channels through which the qubits pass. The source Charles H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin. Experimental quantum cryptography. Journal of cryptology, 5:3-28 and Umesh Vazirani and Thomas Videck. Fully device-independent quantum key distribution. Physical Review Letters, 113(14), Sep 2014 provides example implementations for evaluating the first metric and the second metric.

For example, quantum state tomography can be used to determine the fidelity of the first and second metrics. For example, quantum state tomography can be used to construct the density matrices ρ ₁ and ρ ₂ , e.g., using a series of measurements performed in different bases, and to estimate the fidelity. The first and second metrics can be evaluated using a metric determination system. The metric determination system may or may not be part of the third-party quantum computing system. For example, the metric determination system can use quantum state tomography to construct the density matrices ρ ₁ and ρ ₂ , e.g., using a series of measurements performed in different bases, and to estimate the fidelity.

In one example, the trained machine learning model can be a classical machine learning model such as a deep neural network. Alternatively, the trained machine learning model can be a quantum machine learning model such as a quantum neural network (QNN).

The quantum communication protocol can be, for example, the BB84 protocol or the Eckert protocol E91. The data exchange system can be configured to share information between the sender node and the receiver node in accordance with the BB84 protocol. The quantum communication protocol can be, for example, a single-qubit-based protocol or an entangled-state-based protocol. The single-qubit-based protocol can be referred to as a prepare-and-measure (P&M) protocol.

In one example, the information may be shared between the sender quantum computer system and the receiver quantum computer system by at least: sending qubits by the sender quantum computer system to the receiver quantum computer system. The sender quantum computer system may prepare each qubit in a corresponding computational basis state before sending the prepared qubit to the receiver quantum computer system via the noisy quantum channel. The states of the prepared qubits provide the information shared between the sender quantum computer system and the receiver quantum computer system. This example may be advantageous because it allows for seamless integration of the present subject matter into existing communication protocols, e.g., the quantum communication protocol may be the BB84 protocol. For example, the sender quantum computer system may prepare the qubit using predefined bases. To encode or prepare a qubit, the sender quantum computer system may, for example, select one of the predefined bases and prepare the qubit in a computational basis state using the selected basis. The receiving quantum computer system can measure the prepared qubit once it has been received over the noisy quantum channel by selecting a basis from the predefined basis sets and using the selected basis to measure the prepared qubit received at the receiving quantum computer system. This example can enable information sharing according to the single-qubit-based protocol.

In one example, the information can be shared between the sender quantum computer system and the receiver quantum computer system using entanglement. To this end, a two-qubit system can be defined for each qubit pair of a group of qubit pairs, with one qubit of the two-qubit system being part of the sender quantum computer system and the other qubit being part of the receiver quantum computer. systems. The state of the two-qubit system can be an entangled state. The entangled state of the two-qubit system can, for example, be one of the Bell states, meaning that the sender quantum computer system and the receiver quantum computer system can each receive a photon of a polarization-entangled pair.

The present subject matter can utilize the entangled state of the two-qubit system to transmit or share information between the sender quantum computer system and the receiver quantum computer system. Information can be teleported from the sender's qubit to the receiver's qubit using entanglement. For example, the two qubits can be entangled in such a way that when a particular property is measured in one qubit, the opposite state can be immediately observed in the entangled qubit.

The entangled state can be provided as a distributed entangled state, such that the entangled qubit pair is located at different locations, i.e., in the sender quantum computer system and the receiver quantum computer system, respectively. The distributed entangled state between the qubit pair can be formed, for example, by first forming the entangled state of the qubit pair locally in the sender quantum computer system and then sending one of the qubits of the pair from the sender quantum computer system to the receiver quantum computer system. The entangled state can be formed, for example, by applying a CNOT operation to the qubit pair. Thus, to share information between the sender quantum computer system and the receiver quantum computer system, multiple distributed entangled states can be generated using the respective qubit pairs. The use of entanglement can further secure the sharing of information within the meaning of the present subject matter. In one example, the quantum communication protocol can be an entangled QKD protocol, e.g., B. an entangled BB84 variant.

In one example, the sender quantum computing system and the receiver quantum computing system may be further configured to communicate over a classical public channel, e.g., to exchange public data such as the fundamentals used to prepare or measure the qubits. The third-party quantum computing system may be configured to intercept and receive the data transmitted over the classical public channel. The third-party quantum computing system may use this intercepted information, for example, to determine or improve the attack configuration and to determine the first metric.

When generating training data for training the machine learning model, the security boundaries used by the quantum communication protocol can be used. The quantum communication protocol can control the security of the shared information by taking into account the noise of the noisy quantum channel. To do so, the quantum communication protocol can use security boundaries adapted to the noise model of the noisy quantum channel. Indeed, the security boundaries can be influenced by noise. In particular, different types of noise can affect the security boundaries differently. For example, the security boundaries can be defined for different noise models using a theoretical method through theoretical analysis, a simulation method through model creation and simulation of the modeled systems, or a statistical method through data analysis and the application of statistical procedures to identify patterns. This definition of the security boundaries can make it possible to create the training dataset depending on the noise model.

A security limit can be specified for the reception of qubits at the receiving node. This security limit can be referred to, for example, as a fault tolerance limit. The fault tolerance limit can refer to a value or a range of values. The fault tolerance limit can refer to a value or a range of values for an error rate, a reception success, or a fidelity. The fault tolerance limit can, for example, represent a maximum error rate in the transmission of quantum information or a minimum degree of success in the reception of qubits that should not be exceeded for the secure transmission of the information; otherwise, the communication can be classified as insecure. A low error rate can indicate high accuracy of the transmitted qubits, while a high reception success can indicate the ability to reliably detect and measure these qubits. Thus, a higher reception success probability can indicate a lower probability of error in the transmission and measurement of qubits. Thus, a higher reception success can be associated with a lower error rate. In one example, the error tolerance limit may represent an error caused by a maximum listening level and the noise.

The present subject matter may further use another security boundary representing eavesdropping. This security boundary may be referred to as an attack success boundary. The attack success boundary may be used to evaluate the security of the quantum communication protocol. The attack success boundary may indicate the degree of success of a (simulated) attack or eavesdropping by the third party. The attack success boundary may refer to a value or a range of values. The attack success boundary may refer to a value or a range of values for the fidelity or the degree of success of the eavesdropping attack. The degree of success of the attack may be assessed based on the states of the intercepted qubits determined by the third-party quantum computing system. The states determined by the third-party quantum computing system may be compared with the prepared states of the intercepted qubits to evaluate the success of the attack. Once the intercepted qubits reach the receiving quantum computer system, the states of the intercepted qubits can be measured on the receiving quantum computer system, and the measured states can be compared with the prepared states of the intercepted qubits to assess the degree of reception success on the receiving quantum computer system. The degree of success of the attack can be represented by the first metric. The degree of reception success can be represented by the second metric.

Training the machine learning model

In one example, the machine learning model may be trained on a training dataset. The training dataset includes multiple entries. Each entry of the entries may be associated with a specific data exchange system. Each entry of the entries may include values of the set of parameters describing the associated given data exchange system, the noise model, and a label indicating the security of the given data exchange system for performing data sharing according to the quantum communication protocol. For example, an entry may be specified as a tuple as follows: {["values of the set of parameters", "noise model"], "label"}. The noise model may specify the noise of the noisy quantum channel of the entry's data exchange system. The noise model may be specified in the form of a number or other type of input whose value indicates the type of noise to which the quantum channel is exposed. In one example, the entries may comprise subsets of entries, where each subset of entries of the subsets may represent the same data exchange system used to share different information or to share the same type of information but at different times. Each pair of different data exchange systems represented in the training dataset may differ by one or more parameters of the set of parameters and/or by the noise model used. This may result in a large training dataset representing different configurations of the shared systems. This may enable a reliable and accurate trained model, which in turn enables secure communication of data over quantum channels.

In one example, the training dataset may be created by deploying a quantum simulator to simulate various systems for sharing data over noisy quantum channels. The quantum simulator may be used to evaluate the set of parameters for multiple simulated systems simulated by the quantum simulator under various noise conditions. For each simulated system, it may be determined whether the simulated system is safe or unsafe for sharing information. Each simulated system may include a simulated sender node and a simulated receiver node connected via a simulated noisy quantum channel, and a simulated third-party quantum computing system, wherein the simulated noisy quantum channel is subject to one or more types of noise.

In one example, the quantum simulator's determination of whether the simulated system is safe or unsafe is performed by receiving input, e.g., from a user of the quantum simulator, indicating whether the simulated system is safe or unsafe. That is, the user input for a particular simulated system can be used as a label for the simulated system in the training dataset.

In one example, the quantum simulator determines whether the simulated system is secure or insecure using a security proof procedure. The security proof procedure may, for example, be performed by the quantum simulator. The security proof procedure comprises: determining an attack configuration for third-party access to the noisy quantum channel of the simulated system, wherein the attack configuration is defined by at least one quantum circuit system with specific parameters and the attack success limit, wherein the quantum circuit system is configured to intercept a qubit on the noisy quantum channel and Determine the state of the intercepted qubit without destroying it and send the qubit to the receiver node via the noisy quantum channel, defining a first metric representing a degree of success of an attack by the third party, and the second metric indicating a degree of reception success at the receiver node; use the quantum circuit system to evaluate the first metric by intercepting at least qubits on the noisy quantum channel, and use the receiver node to evaluate the second metric; determine whether the second metric satisfies the fault tolerance limit and whether the first metric satisfies the attack success limit. If the second metric satisfies the fault tolerance limit and the first metric satisfies the attack success limit, the simulated system is determined to be insecure. If the second metric does not satisfy the fault tolerance limit and the first metric satisfies the attack success limit, the simulated system can be determined to be insecure. It can be determined that the simulated system is secure if the second metric satisfies the fault tolerance limit and the first metric does not satisfy the attack success limit.

The quantum circuit system simulated and used by the security proof procedure to generate the training data may be the quantum circuit system used by the third party in the inference phase. The quantum communication protocol simulated and used by the security proof procedure to generate the training data may be the quantum communication protocol used by the data exchange system in real time (in the inference phase).

The value of the first metric can be compared to the attack success threshold (first comparison) to determine whether the value of the first metric satisfies the attack success threshold for the simulated system. The value of the first metric satisfies the attack success threshold, which may mean that the attack is successful. For example, the attack success degree may satisfy the attack success threshold, which may mean that the attack success degree is higher than the attack success threshold. For example, the fidelity metric (representing the attack success degree) may be higher than 80%, where 80% may be the attack success threshold. The value of the second metric can be compared to the fault tolerance threshold (second comparison) to determine whether the value of the second metric satisfies the fault tolerance threshold for the simulated system. The value of the second metric satisfying the fault tolerance threshold may mean that the reception of information at the receiving node is successful (e.g., secure). For example, the degree of reception success at the receiver node may satisfy the fault tolerance limit, meaning that the degree of reception success at the receiver node is higher than the fault tolerance limit, where the fault tolerance limit may be a minimum degree of reception success. In another example, if the fault tolerance limit is a maximum error rate, the reception error rate at the receiver node satisfies this limit if it is smaller than the fault tolerance limit. For example, the error rate at the receiver node may be less than 10%, where 10% may be the fault tolerance limit.

For example, the security proof procedure may not only use the results of the second comparison to decide on the security of the quantum communication protocol in the simulated system, but rather it may use the results of both the first and second comparisons to decide on the security of the quantum communication protocol. For example, the simulated system may be classified as insecure if the second metric satisfies the fault tolerance limit and the first metric satisfies the attack success limit. In another example, the simulated system may be classified as insecure if the second metric does not satisfy the fault tolerance limit and the first metric satisfies the attack success limit. The simulated system may be classified as secure if the second metric satisfies the fault tolerance limit and the first metric does not satisfy the attack success limit.

The subject matter can thus enable two or more remote parties to communicate with each other securely. This communication can be useful in a wide range of applications where security is critical, such as financial transactions, government communications, and military operations.

Examples of the application of the safety case procedure

As described in the example above, the quantum simulator can be used to build the training dataset by simulating various systems and predicting their security (labeling) using the security proof procedure. For example, the quantum simulator can be configured to simulate the quantum communication protocol using a model of a real data exchange system that enables the communication of quantum information in accordance with various noise models. For example, the quantum simulator can be configured to predict the parameters for individual components and sub-protocols in the system, including the quantum channel and the communicating parties. The quantum simulator can, for example, be implemented as a software application.

The present subject matter may utilize advantageous techniques to provide various (simulated) attack configurations of the third-party quantum computing system, enabling reliable proof of the security of the quantum communication protocol using the noisy quantum channel of the simulated system. For this purpose, one or more attack configurations may be defined using offline analysis and the quantum simulator. The offline analysis may be referred to as an attack simulation method.

In a first optimization example, the attack simulation method may use the quantum simulator to optimize the specific parameters of the third-party quantum computing system to improve the attack success rate. The attack simulation method may comprise defining a quantum circuit system comprising at least the intercepted qubit and one or more additional qubits, and performing one or more quantum operations with the specific parameters, wherein the quantum operation(s) allow determining the state of the intercepted qubit, e.g., without affecting the prepared state of the intercepted qubit. The attack simulation method may further comprise evaluating the first metric using the determined/estimated states of the intercepted qubits. The attack simulation method may be repeated multiple times, using different values of the specific parameters at each iteration. The repetition may be performed until a desired target of the first metric is reached, where the values of the parameters that provide the desired target are provided as optimal parameters, where the desired target is defined according to the noise model of the noisy quantum channel accessed by the third-party quantum computing system. Alternatively, the repetition may be performed a predefined number of times, the resulting first metric values may be compared, and the values of the parameters that provide the best first metric may be provided as the optimal parameters. In this way, the attack simulation method may make it possible to obtain optimized values for the specific parameters. These optimized values (and the associated quantum circuit system) may be used by the present security proof method to prove the security of the shared information between the sender quantum computing system and the receiving quantum computing system of the simulated system. The first optimization example may be performed for different noise models. That is, the quantum circuit system may be optimized for different types of noise.

In a second optimization example, the attack simulation method may use the quantum simulator to optimize the specific parameters of the third-party quantum computing system to improve the attack success through machine learning. For this purpose, an objective function may be defined. The attack simulation method may be repeated multiple times, with different values of the specific parameters being set for each iteration based on the evaluated objective function. The iteration may be performed until the objective function meets a convergence criterion. This example may enable a precise determination of the optimal parameters. This may further improve the security proof according to the present subject matter. The objective function may be defined based on the type of first metric used and the noise model. The second optimization example may be performed for different noise models. That is, the quantum circuit system may be optimized for different types of noise.

In one example, the second metric may be a fidelity between the state of the prepared qubit, as prepared by the sender node, and the measured state of the qubit received and measured by the receiver quantum computing system of the simulated system. The state of the prepared qubit may be represented by a density matrix ρ ₁ , and the state measured by the receiver quantum computing system may be represented by a density matrix ρ ₂ . The second metric may thus be defined as follows: $F_1\left({\mathrm{<figure-callout\; id="1"\; label="\rho "\; filenames="DE102023129996A1\_0019.png"\; state="\{\{state\}\}">\rho </figure-callout>}}_1,{\rho }_2\right)={\left(\text{<figure-callout id="1" label="tr ρ" filenames="DE102023129996A1\_0019.png" state="{{state}}">tr</figure-callout>}\sqrt{\sqrt{{\rho }_{}}}\sqrt{\sqrt{{}_1}{\rho }_2\sqrt{{\rho }_1}}\right)}^2.$

In one example, the first metric (F ₂ ) can be the fidelity between the state of the intercepted qubit, as determined or estimated by the third party, and a state of the prepared qubit, as prepared by the sender node of the simulated system. Thus, the first metric can be defined as follows: $F_2\left({\mathrm{<figure-callout\; id="1"\; label="\rho "\; filenames="DE102023129996A1\_0019.png"\; state="\{\{state\}\}">\rho </figure-callout>}}_1,{\rho }_2\right)={\left(\text{<figure-callout id="1" label="tr ρ" filenames="DE102023129996A1\_0019.png" state="{{state}}">tr</figure-callout>}\sqrt{\sqrt{{\rho }_{}}}\sqrt{\sqrt{{}_1}{\rho }_2\sqrt{{\rho }_1}}\right)}^2.$

For example, the first metric can have the value 1 if the states are identical and the value 0 if both are orthogonal. The third-party quantum computer system of the simulated system can provide a quantum circuit system to ensure its fidelity and the fidelity at the receiver as close to 1 as possible. In this case, the attack can only be detected with a low probability. For example, if the quantum communication protocol is the BB84 protocol, four different states can be selected with equal probability. In this case, the average fidelity (e.g., the fidelity is measured for all different states and averaged across four different states) can be used as the first metric for the third-party quantum computing system and as the second metric for the receiving quantum computing system.

wobei X die Zufallsvariable sein kann, die den Bits im Quantensystem des Senders zugeordnet ist, und Y die Zufallsvariable sein kann, die den Bits im Quantensystem des simulierten Systems zugeordnet ist, wobei p(x,y) die gemeinsame Wahrscheinlichkeit ist, und p(x) und p(y) die individuellen Wahrscheinlichkeiten sind.In one example, the first metric used in the safety case procedure may be the common information. The common information may be defined, for example, as follows: $I\left(X,Y\right)={\displaystyle \sum {}_x{\displaystyle \sum {}_{y}p\left(x,y\right){\text{log}}_2\left(\frac{p\left(x,y\right)}{p\left(x\right)p\left(y\right)}\right),}}$

where X can be the random variable associated with the bits in the sender's quantum system, and Y can be the random variable associated with the bits in the simulated system's quantum system, where p(x,y) is the joint probability, and p(x) and p(y) are the individual probabilities.

For example, two random bits b1, b2 ∈ [0, 1] are input to the quantum channel, and the output can be the XOR value b1⊕b2. The corresponding probabilities are listed in the following table: input 00 01 10 11 Output 0 ¼ 0 0 ¼ Exit 1 0 ¼ ¼ 0

For example, input 00 occurs together with output 0 with probability 1/4. Thus, the value of the transinformation can be 1, i.e., of two possible information bits, 1 bit is transmitted over the channel. However, no information about the individual bits can have been received, because even after knowing b1⊕b2, the values of b1 and b2 are still equally distributed. Nevertheless, the information about the value of b1⊕b2 can be valuable to an attacker (or eavesdropper), because it can allow them to limit the search space in a brute-force search from 4 possibilities to 2.

For example, the accuracy of the receiving quantum computer system of the simulated system can be denoted as F ₁ and the fidelity for the third-party quantum computer system of the simulated system can be denoted as F ₂ . The objective function of the second optimization example can be defined, for example, as follows: - F ₂ +10 × (F ₁ - Objective) ² , where "Objective" is a predefined target value for the fidelity F ₁ taking into account the noise model. Alternatively, the objective function can be defined as - F ₂ - F ₁ . The shared information for the third-party quantum computer system of the simulated system can be defined as I ₂ . In this case, the objective function can be defined, for example, as follows: I ₂ +10 × (F ₁ - Objective) ² .

The first and second metrics can be evaluated using a metric determination system of the simulated system. The metric determination system may or may not be part of the simulated system's third-party quantum computing system. For example, the metric determination system may use quantum state tomography to construct the density matrices ρ ₁ and ρ ₂ , e.g., with a series of measurements performed in different bases, and estimate the fidelity.

In one example, the quantum communication protocol may be the quantum key distribution (QKD) protocol, where the shared information includes a key. The QKD protocol may be, for example, the BB84 protocol. The transmitted qubits may be photons prepared in computational basis states, where the computational basis states may be horizontal and vertical polarization states or diagonal polarization states.

The present subject matter can further improve the proof of security of the quantum communication protocol using the noisy quantum channel. To this end, various structures of the quantum circuit system of the third-party quantum computer system of the simulated system can be used to intercept the qubit and determine the state of the intercepted qubit.

In one example, various quantum circuit systems may be defined, and for each quantum circuit system, the quantum circuit system may be applied to intercept the qubit on the quantum channel of the simulated system and evaluate the first metric. The quantum circuit system having the best value of the first metric may be selected and used to perform the security proof method according to the present subject matter. Each quantum circuit system may include the intercepted qubit and a certain number of additional qubits and perform a series of quantum operations, including one controlled operation and zero or more additional quantum operations. The parameters The parameters (e.g., rotation angle) of the set of quantum operations can be the specific parameters of the quantum circuit system. The number of additional qubits and additional quantum operations of each quantum circuit system can, for example, be randomly selected or user-defined.

In a first circuit example, the quantum circuit system comprises the intercepted qubit and one or more qubits. The quantum circuit system is configured to perform a sequence of one or more quantum operations on the qubits to determine the state of the intercepted qubit without destroying the state of the intercepted qubit.

In a second circuit example, the quantum circuit system comprises the captured qubit and a target qubit. The target qubit is prepared in an initial basis state. Furthermore, the sequence of one or more quantum operations is a single quantum operation that transforms the initial basis state of the target qubit depending on the state of the captured qubit without destroying the state of the captured qubit. The state of the captured qubit is determined or estimated from a state of the target qubit measured after applying the transformation.

In a third circuit example, the quantum communication protocol can be a QKD protocol such as BB84. According to this quantum communication protocol, the sender quantum computer system can send the bases used to prepare the intercepted qubits to the receiver quantum computer system via a classical public channel. The third-party quantum computer system can be configured to intercept the data transmitted via the classical public channel and have access to the used bases. The third-party quantum computer system can be further configured to store the intercepted qubits, for example, for later operation. The attack simulation method can exploit this to control the quantum circuit system to perform a basis-dependent operation using the stored qubit and the information obtained about the bases. For this purpose, the quantum circuit system comprises the intercepted qubit and a target qubit. The target qubit is prepared in an initial basis state. The sequence of one or more quantum operations includes a controlled quantum operation that transforms the initial basis state of the target qubit depending on the state of the captured qubit, and another quantum operation that transforms the state of the transformed target qubit, taking into account the basis used to prepare the captured qubit. The state of the captured qubit can be determined or estimated from a state of the target qubit measured after applying the two transformations, without destroying the state of the captured qubit.

In a fourth circuit example, the quantum circuit system comprises the intercepted qubit, a first target qubit, and a second target qubit. The sequence of quantum operations includes a controlled quantum operation that allows the state of the first target qubit to be determined depending on the state of the intercepted qubit, and a quantum operation that allows the state of the second target qubit to be determined based on a specific computational basis. The quantum operations can be performed by the quantum circuit system without destroying the state of the intercepted qubit.

In a fifth circuit example, the quantum circuit system can be configured to create one or more approximate state copies of the intercepted qubit. This quantum circuit system can make it possible to create a state that has the highest possible fidelity while preserving the fidelity for the receiving node as well as possible. The quantum circuit system can comprise the intercepted qubit with the state ρ and an additional qubit, which can be prepared, for example, in a basis state, e.g., |0 > . The quantum circuit system can be configured to perform a series of one or more quantum operations on the input state ρ⊗|0 >< 0| to obtain a state ρ̃⊗ρ̃, where ρ̃ is the approximate state copy of the state ρ of the intercepted qubit. The approximate copy ρ̃ can be received by the receiving quantum computer system, but since it is an approximate copy, the fidelity at the receiving node can still be high. The approximate copies can be used to estimate the first and second metrics. The approximate copy ρ̃ can be compared with the original state ρ to estimate the first metric. The approximate copy ρ̃ received at the receiving quantum computer system can be compared with the original state ρ to estimate the second metric.

In one example, the present method can be implemented in a quantum repeater. This can enable seamless integration of the present subject matter into existing systems.

In one example, each quantum circuit system of the above circuit examples may be further used to determine the first metric and configured to send the intercepted qubit to the receiver node via the noisy quantum channel.

The computer system according to the present subject matter may be a classical computer system or a hybrid classical quantum computer system. The computer system may be configured to control the third party and the receiver node to determine the values of the first and second metrics, respectively. The computer system may be configured to evaluate the set of parameters, excluding the first and second metrics, using user input or using the metadata file. The metric determination system of 1 is an example of a computer system.

1 is a diagram of a system 100 according to an example of the present subject matter. The system 100 includes a quantum communication system 110 and a metric determination system 105. The quantum communication system 110 includes a sender quantum computer system 101 and a receiver quantum computer system 102 configured to exchange or share information over a noisy quantum channel 104. The quantum communication system 110 further includes a third-party quantum computer system 103 configured to intercept qubits on the noisy quantum channel 104, estimate the states of the intercepted qubits, e.g., without destroying the states of the intercepted qubits, and transmit the qubits over the noisy quantum channel 104 to the receiver node 102. For this purpose, the third-party quantum computer system 103 may comprise a quantum circuit system that provides an experimental implementation of the schematically illustrated circuit of the 5B-5D and 6B The third-party quantum computing system 103 may be located at any point in the noisy quantum channel. For example, the third-party quantum computing system 103 may be located near the receiver node 102; for example, the third-party quantum computing system 103 may or may not be part of the receiver node 102.

The metric determination system 105 may comprise a classical computer or a quantum computer and may communicate with components of the quantum communication system 110. The metric determination system 105 may be configured to control the operation of the third-party quantum computing system 103. The metric determination system 105 may cause the quantum circuit system of the third-party quantum computing system 103 to intercept one or more qubits transmitted on the noisy quantum channel 104 and perform corresponding measurements to determine output information that allows the metric to be determined, such as the first metric. The metric determination system 105 may be configured to control the operation of the receiver node 102 to determine the second metric.

The metric determination system 105 may include a trained machine learning (ML) model 111. The machine learning model 111 is configured to receive as input the noise model and the values of the set of parameters evaluated for a given system (such as system 110), where the given system includes a given receiver node (such as receiver node 102) and a given transmitter node (such as transmitter node 101) configured to share information over a given noisy quantum channel connecting the receiver node to the transmitter node in accordance with the quantum communication protocol and a noise model of the noise of the noisy quantum channel. 2 shows an example of the implementation of the machine learning model 111. The machine learning model 111 may, for example, be a neural network, but is not limited to this. The given system may, for example, be a QKD key sharing system. The input of the machine learning model 111 may, for example, include: L system parameters SP ₁ through SP _L , fidelities F ₁ and F ₂ of the given system, and the noise model N _m indicating the noise of the noisy quantum channel. The output of the machine learning model 111 may, for example, be a value indicating whether the given data exchange system is secure or insecure. The trustworthiness determined for the receiver may be denoted as F ₁ and the fidelity determined for the third party may be denoted as F ₂ . The noise model N _m may, for example, For example, it can be encoded using techniques such as one-hot encoding to convert it into a numerical format that the ML model 111 can understand.

3 is a flowchart of an example method for sharing information between a sender node and a receiver node in accordance with a quantum communication protocol. For illustration, the 3 described method using the method described in 1 The transmitter node can be implemented in the system shown, but is not limited to this implementation. For example, the transmitter quantum computer system 101 and the receiver node may be the receiver quantum computer system 102.

The set of parameters may be evaluated for the data exchange system 110 in step 121. Furthermore, the noise model of the noise of the noisy quantum channel 104 of the data exchange system may be determined, for example, in step 121. The noise model may be determined, for example, by receiving user input indicating the noise model of the noise of the noisy quantum channel 104. Alternatively, the noise model may be determined, for example, by using a metadata file describing the data exchange system 110. The system parameters of the set of parameters may be evaluated, for example, based on the metadata file or by receiving user input with values of the system parameters. The evaluated set of parameters and the noise model indicating the noise of the noisy quantum channel 104 may be input to the machine learning model 111 in step 123. In response to the input, a prediction of the security of system 110 may be obtained from machine learning model 111 in step 125. The quantum communication protocol may be aborted in step 129 if (query step 127) the system is predicted to be insecure. The abort may result in the shared information not being used. If system 110 is predicted to be secure, the shared information may continue to be used by the sender and receiver nodes.

In one example, evaluating the set of parameters in step 121 may include receiving values of the system parameters of the set of parameters and evaluating the first metric using the third-party quantum computing system and evaluating the second metric using the receiver's quantum computing system. For example, the metric determination system may control the third-party quantum computing system and the receiver's quantum computing system to obtain values of the density matrices that can be used to evaluate the respective fidelities. The evaluation of the set of parameters may occur during the propagation of the information, e.g., by using a portion of the information to be propagated. Alternatively, the evaluation of the set of parameters may be performed prior to the propagation of the information, e.g., by propagating test information.

4 is a flowchart of a security proof procedure for determining whether a simulated system is safe or unsafe for sharing information. The simulated system can be provided by the quantum simulator. The simulated system can, for example, be the one in 1 system shown.

In step 201, an attack configuration for the third party's access to the quantum channel may be determined. The attack configuration is defined by at least one quantum circuit system with specific parameters and an attack success threshold, wherein the quantum circuit system is configured to intercept a qubit on the quantum channel, determine the state of the intercepted qubit, and send the qubit (or an approximate copy thereof) to the receiving node. The 5B-5D show examples of attack configurations.

A first metric representing the degree of success of an attack by the third party and a second metric indicating the degree of reception success at the receiving node may be defined in step 203. For example, the first and second metrics may be user-defined metrics. e.g., an input may be received in step 203 that provides the definition of the first and second metrics. In another example, the first and second metrics may be defined by (e.g., randomly) selecting from a list of predefined metrics.

The quantum circuit system may be used in step 205 to measure or determine the first metric by intercepting at least qubits on the quantum channel. The second metric may be evaluated in step 205 using the receiver node.

In step 207, it may be determined whether the second metric satisfies the fault tolerance limit and whether the first metric satisfies the attack success limit.

If the second metric satisfies the fault tolerance limit and the first metric satisfies the attack success limit, it may be determined in step 209 that the simulated system is unsafe. If the second metric does not satisfy the fault tolerance limit and the first metric satisfies the attack success limit, it may be determined that the simulated system is unsafe. It may be determined (step 211) that the simulated system is safe if the second metric satisfies the fault tolerance limit and the first metric does not satisfy the attack success limit.

5A is a diagram illustrating an example of a quantum communication system according to an example of the present subject matter. Specifically, the quantum communication system is represented by a quantum circuit 300. The quantum circuit 300 represents a qubit q0, which is transmitted from the transmitter (Alice) 301 to the receiver (Bob) 302. The qubit q0 can be intercepted by the third-party quantum computer system (Eva) 303 and used as a target qubit for another qubit q1 of the quantum circuit 300. The quantum circuit 300 further comprises measuring devices for measuring the qubits q0 and q1, wherein the qubit q0 is measured at the receiver 302 and the qubit q1 is measured at the third-party quantum computer system 303. The third-party quantum computer system 303 can comprise a quantum circuit system as described in 5B , 5C or 5D The quantum circuit systems of 5B and 5C can allow the interception of the qubit and the estimation of its state without destroying or altering its state, i.e. the receiver can receive the qubit as it was prepared by the sender.

schematically shows an example of a quantum circuit system 310 for the third-party quantum computing system according to an example of the present subject matter. The quantum circuit system 310 may consist of a controlled rotation on Eve's system, while Alice's and Bob's systems serve as the control system. The quantum circuit system 310 may be configured to perform a rotation along the y-axis on qubit q1 using angle α, where angle α is the parameter of the quantum circuit system 310. The rotation may use qubit q1 as the target and the intercepted qubit q0 as the control qubit.

5C schematically shows an example of a quantum circuit system 311 for the third-party quantum computing system according to an example of the present subject matter. The quantum circuit system 311 is an extension of the controlled rotation of the quantum circuit system 310 on Eva's system by a different, but uncontrolled, operation on Eva's system. The quantum circuit system 311 may be configured to perform a first rotation along the y-axis on the qubit q1 using the angle a and using the qubit q0 as the target qubit, followed by the uncontrolled rotation along the y-axis using the angle b, where the angles a and b are the parameters of the quantum circuit system 311.

5D schematically shows an example of a quantum circuit system 312 for the third-party quantum computing system for the BB84 protocol in accordance with an example of the present subject matter. The quantum circuit system 312 may be configured to perform a rotation along the y-axis on qubit q1 using the angle π/2 followed by a CNOT operation using qubit q1 as the target qubit and q0 as the target. The rotation may use qubit q1 as the target and the intercepted qubit q0 as the control qubit. The quantum circuit system 312 may be configured to create approximate copies of the intercepted qubit. This quantum circuit system 312 may enable the establishment of a state that has the highest possible state quality with the transmitted state, such that at the same time the state quality is also preserved as best as possible for the receiver. The quantum circuit system may comprise the trapped qubit with state ρ and an additional qubit, which may be prepared in a basis state |0>. The quantum circuit system may be configured to perform a series of one or more quantum operations on the input state ρ⊗|0 >< 0| to obtain a state ρ̃⊗ρ̃, where ρ̃ is the approximate state copy of the state ρ of the trapped qubit.

$$

Jeder der kopierten Zustände kann mit dem jeweiligen Originalzustand verglichen werden. Die erste und die zweite Metrik können unter Verwendung einer partiellen Verfolgung der Näherungszustände ausgewertet werden, um den Vergleich des Näherungszustands am Empfängerknoten und bei der dritten Partei mit dem ursprünglichen Zustand des übertragenen Qubits zu ermöglichen. Außerdem kann es sein, dass die Näherungszustände, die in der spezifischen Basis definiert sind, nicht orthogonal zueinander sind und nicht fehlerfrei voneinander unterschieden werden können. Zur Unterscheidung der Näherungszustände kann z. B. das Pretty Good Measurement (PGM) verwendet werden. Dazu können die Dichtematrizen ρ_i mit den zugehörigen Wahrscheinlichkeiten p_i zu einer Matrix G addiert werden und dann die Wurzel aus der Pseudoinverse von G berechnet werden. Dies kann die Operatoren ${\mathrm{\Pi }}_i=p_i\sqrt{G^{-1}}{\rho }_i\sqrt{G^{-1}}$

$$

eines positiven Operator-bewerteten Maßes (POVM) auf dem von den Zuständen aufgespannten Raum bereitstellen. Wenn der simulierte Angriff in der Lage ist, die ungefähre Kopie des Zustands zu speichern, bis Alice und Bob Informationen über die gewählte Basis austauschen, kann die dritte Partei Operationen auf dem gespeicherten Zustand durchführen, die von der Basis abhängen. Da Bob und Eva den gleichen Zustand erhalten können, ist zu erwarten, dass Bob und Eva auch die gleiche Erfolgswahrscheinlichkeit bei der Identifizierung der übertragenen Zustände haben können. In diesem Fall kann die Messung in einer der beiden Basen durchgeführt werden: $B_1=\left\{\sqrt{\frac{1}{2}}\left(\begin{array}{l}1\\ 1\end{array}\right),\sqrt{\frac{1}{2}}\left(\begin{array}{l}1\\ -1\end{array}\right)\right\}$

oder $$

$B_2=\left\{\sqrt{\frac{1}{2}}\left(\begin{array}{l}1\\ i\end{array}\right),\sqrt{\frac{1}{2}}\left(\begin{array}{l}1\\ -i\end{array}\right)\right\}.$

The copied states can be defined in a specific basis, in which the original states of the transferred qubit are defined according to the BB84 protocol. The basis states can be, for example: $\sqrt{\frac{1}{2}}\left(\begin{array}{l}1\\ 1\end{array}\right),\sqrt{\frac{1}{2}}\left(\begin{array}{l}1\\ i\end{array}\right),\sqrt{\frac{1}{2}}\left(\begin{array}{l}1\\ -1\end{array}\right)\sqrt{\frac{1}{2}}\left(\begin{array}{l}1\\ -i\end{array}\right).$

$$

Each of the copied states can be compared with the respective original state. The first and second metrics can be evaluated using partial tracking of the approximate states to enable comparison of the approximate state at the receiving node and at the third party with the original state of the transmitted qubit. Furthermore, the approximate states defined in the specific basis may not be orthogonal to each other and cannot be accurately distinguished from each other. To distinguish the approximate states, one can use, for example, Pretty Good Measurement (PGM). To do this, the density matrices ρ _i with the corresponding probabilities p _i can be added to a matrix G, and then the square root of the pseudoinverse of G can be calculated. This can involve the operators ${\mathrm{\Pi }}_i=p_i\sqrt{G^{-1}}{\rho }_i\sqrt{G^{-1}}$

$$

a positive operator-valued measure (POVM) on the space spanned by the states. If the simulated attack is able to store the approximate copy of the state until Alice and Bob exchange information about the chosen basis, the third party can perform operations on the stored state that depend on the basis. Since Bob and Eve can receive the same state, it is expected that Bob and Eve can also have the same probability of success in identifying the transferred states. In this case, the measurement can be performed in either of the two bases. become: ${\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="DE102023129996A1\_0019.png"\; state="\{\{state\}\}">B</figure-callout>}}_1=\left\{\sqrt{\frac{1}{2}}\left(\begin{array}{l}1\\ 1\end{array}\right),\sqrt{\frac{1}{2}}\left(\begin{array}{l}1\\ -1\end{array}\right)\right\}$

or $$

$B_2=\left\{\sqrt{\frac{1}{2}}\left(\begin{array}{l}1\\ i\end{array}\right),\sqrt{\frac{1}{2}}\left(\begin{array}{l}1\\ -i\end{array}\right)\right\}.$

In an example where the third-party system is configured to store the intercepted qubit, the simulated attack can be divided into two parts: The first part is the interaction between Alice and Bob's system and the third-party system, which can be stored. After revealing the selected bases, the third-party system can perform a base-dependent operation on the stored qubit before measuring the qubit. This can be done, for example, using the circuit from 6A be realized.

6A is a diagram illustrating a quantum communication system in accordance with an example of the present subject matter. Specifically, the quantum communication system is represented by a quantum circuit 400. The quantum circuit 400 represents a qubit q0 transmitted from the transmitter (Alice) 401 to the receiver (Bob) 402. The qubit q0 can be intercepted by the third-party quantum computing system (Eva) 403 and used as a target qubit for another qubit q1. The quantum circuit 400 further comprises measuring devices for measuring the qubits q0 and q1, wherein the qubit q0 is measured at the receiver 402 and the qubit q1 is measured at the third-party quantum computing system 403. The third-party quantum computing system 403 can comprise a first quantum circuit system as shown in 5B or 5C Furthermore, the third-party quantum computer system 403 may include two second quantum circuit systems described in 6B and each associated with a specific basis (e.g., if the qubits are photons, the basis can include horizontal and vertical polarization states).

In this example, the intercepted qubit can be stored or secured by the third-party quantum computing system. Furthermore, the third-party quantum computing system can have access to the basis used by the sender to prepare the state of the intercepted qubit. This can be the case, for example, with the BB84 protocol, where the bases are sent over a classical public channel and intercepted by the third-party quantum computing system.

As in 6A As indicated, the quantum circuit 400 may enable a sequence of at least two operations (rotations around the y-axis) to be performed on the qubit q1, e.g., the operation implemented by the third-party quantum computing system 403 and the operation 406. The qubit q1 is prepared in an initial basis state. The sequence of quantum operations includes a quantum operation performed by the first quantum circuit system to transform the initial basis state of the qubit q1 depending on the state of the intercepted qubit q0. The sequence of quantum operations further includes another quantum operation that transforms the state of the transformed qubit q1 taking into account the basis used to prepare the intercepted qubit q0. This other quantum operation can be performed by one of the second quantum circuit systems connected to the basis used to prepare the intercepted qubit q0. This other quantum operation can be called a basis-dependent operation. As in 6A As indicated, this basis-dependent operation 406 can still be performed even after Bob's system has measured the qubit q0. The state of the intercepted qubit q0 can be determined by the third-party quantum computer system from a state of the qubit q1 measured after applying the sequence of operations.

6B shows an example of two quantum circuit systems 410 and 411 for the third-party quantum computer system in accordance with an example of the present subject matter. Each of the two quantum circuit systems is in 5C The two quantum circuit systems can be used depending on the basis that Alice's system uses to prepare the intercepted qubit. Since Alice's system can use two bases, these two quantum circuit systems 410 and 411 are dedicated to the two bases. For this purpose, each of the two quantum circuit systems is configured to perform a controlled operation followed by an uncontrolled operation on qubit q1. The controlled operation in the two circuits uses the same angle a, while the uncontrolled operation uses two different angles b and c in the two quantum circuit systems.

7 is a flowchart of a method for optimizing the parameters of the quantum circuit system according to an example of the present subject matter. The parameters may be set to current values in step 501. The quantum circuit system may be used to measure the first metric in step 503. In step 505, it may be determined whether the first metric satisfies a convergence criterion. If the first metric satisfies the convergence criterion, the parameter values may be provided in step 507, e.g., to be used in the method of 4 and 3 ver to be applied. If the first metric does not meet the convergence criterion, the method returns to step 501 to adjust the parameters to other values. For example, the convergence criterion may require that the first metric be within a target range of values, where the target values may be defined according to the noise model.

QUOTES CONTAINED IN THE DESCRIPTION

This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited non-patent literature

• Charles H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin. Experimental quantum cryptography. Journal of cryptology, 5:3-28 [0028]
• Umesh Vazirani and Thomas Videck. Fully device-independent quantum key distribution. Physical Review Letters, 113(14), Sep 2014 [0028]

Claims (19)

A method for sharing information using a data exchange system (100) comprising a sender node (101) and a receiver node (102) using a noisy quantum channel (104) in accordance with a quantum communication protocol, the method comprising: providing a trained machine learning model (111), wherein the machine learning model is configured to receive a noise model of a noisy quantum channel noise of a given system and a set of parameters of the given system to predict whether the given system is secure or unsafe for sharing information according to the quantum communication protocol, wherein the set of parameters indicates a degree of success of a third-party attack and a degree of reception success at the receiver node of the given system and describes the given system; determining (121) a noise model for a noisy quantum channel noise of the data exchange system; Evaluating (121) the set of parameters for the data exchange system for sharing the information; Inputting (123) the evaluated set of parameters and the noise model into the machine learning model, thereby obtaining a prediction of the security of the data exchange system (125); Aborting (129) the quantum communication protocol if the data exchange system is determined to be insecure. Procedure according to Claim 1 , wherein the noise model has at least one of the following features: depolarizing channel noise, amplitude-damping channel noise, phase-damping channel noise, or bit-flip channel noise. Procedure according to Claim 1 or 2 , wherein the degree of success of the attack is assessed using a quantum circuit system, the quantum circuit system being configured to intercept a qubit on the noisy quantum channel and determine the state of the qubit and send the qubit to the receiver node via the quantum channel. Procedure according to Claim 3 , wherein the quantum circuit system comprises the intercepted qubit and one or more qubits, the quantum circuit system being configured to perform a sequence of one or more quantum operations on the qubits to determine the state of the intercepted qubit. Method according to one of the preceding claims, wherein the set of parameters comprises system parameters describing the data exchange system, the system parameters comprising at least one of the following parameters: a distance between the transmitter and receiver nodes, a detector efficiency of a signal detector at the receiver node, design parameters of components of the data exchange system and an amount of information to be shared between the transmitter node and the receiver node. The method of any preceding claim, further comprising: providing a training dataset with entries, each entry containing values of the set of parameters of a given system and the noise model, as well as a label indicating the security of the given system; training the machine learning model using the training dataset, thereby providing the trained machine learning model. Procedure according to Claim 6 , wherein creating the training dataset comprises: providing a quantum simulator, the quantum simulator configured to simulate various systems for sharing information over quantum channels in accordance with the quantum communication protocol and various noise models; using the quantum simulator to evaluate the set of parameters for a plurality of systems simulated by the quantum simulator; for each simulated system, determining whether the simulated system is secure or unsafe, and thereby providing the label for the simulated system. Procedure according to Claim 7 , wherein the determination of whether the simulated system is secure or insecure is performed using a security proof procedure, the security proof procedure comprising: determining an attack configuration for third-party access to the noisy quantum channel of the simulated system, the attack configuration being defined by at least one quantum circuit system with specific parameters and an attack success limit, the attack success limit being defined in accordance with the noise model, the quantum circuit system being configured to intercept a qubit on the quantum channel and to determine the state of the intercepted qubit, the quantum communication protocol providing an error to tolerance limit for the receiver node in accordance with the noise model; defining a first metric representing the degree of success of an attack by the third party and a second metric indicating the degree of reception success at the receiver node; using the quantum circuit system to evaluate the first metric by at least intercepting qubits on the quantum channel and using the simulated receiver node to evaluate the second metric; determining whether the second metric satisfies the fault tolerance limit and whether the first metric satisfies the attack success limit; determining that the simulated system is insecure if the second metric satisfies the fault tolerance limit and the first metric satisfies the attack success limit, or if the second metric does not satisfy the fault tolerance limit and the first metric satisfies the attack success limit; otherwise, determining that the simulated system is secure. The method according to any one of the preceding claims, wherein the machine learning model is a quantum machine learning model or a classical machine learning model. A method according to any one of the preceding claims, comprising: repeatedly: preparing a qubit in a corresponding base state by the sender node; sending the prepared qubit by the sender node via the quantum channel to the receiver node to enable information sharing; wherein the intercepted qubits used to evaluate the degree of success of an attack are the prepared qubits. A method according to any one of the preceding claims, comprising: repeatedly forming an entanglement state between a transmitter qubit in the transmitter node and a receiver qubit; transmitting the receiver qubit by the transmitter node to the receiver node via the quantum channel; wherein the intercepted qubits used to evaluate the degree of success of an attack are the receiver qubits. Method according to one of the preceding Claims 3 until 10 , further comprising: using a quantum simulator to optimize parameters of the quantum circuit system, wherein the optimization comprises repeatedly changing values of the parameters of the quantum circuit system and evaluating the first metric, wherein the repetition is performed to obtain a target value of the first metric; providing the specific parameters of the quantum circuit system as optimized parameters in association with the target value of the first metric. A method according to any one of the preceding claims, wherein the second metric is a fidelity between the state of the qubit received at the receiver node and a state of the prepared qubit, the second metric representing a degree of reception success. A method according to any one of the preceding claims, wherein the first metric is a fidelity between the state of the intercepted qubit and a state of the prepared qubit or a shared information between the sender node and the third party, the first metric representing the degree of success of an attack. A method according to any one of the preceding claims, wherein the quantum communication protocol is a quantum key distribution protocol. The method of any preceding claim, wherein the shared information comprises an encryption key, a token, or a secret. A computer program containing instructions to configure a computer system to carry out the method according to Claim 1 to arrange. A computer system (105) for controlling a data exchange system (100) comprising a sender node (101) and a receiver node (102), wherein the data exchange system is configured for sharing information using a noisy quantum channel (104) in accordance with a quantum communication protocol, wherein the computer system (105) is configured to: provide a trained machine learning model (111), wherein the machine learning model is configured to receive a noise model of a noisy quantum channel noise of a given system and a set of parameters of the given system to predict whether the given system is secure or unsafe for sharing information according to the quantum communication protocol, wherein the set of parameters indicates a degree of success of a third-party attack and a degree of reception success at the receiver node of the given system and describes the given system; determining (121) a noise model for a noise spanning the noisy quantum channel of the data exchange system; evaluating (121) the set of parameters for the data exchange system for sharing the information; inputting (123) the evaluated set of parameters and the noise model into the machine learning model, thereby obtaining a prediction of a security of the data exchange system (125); terminating (129) the quantum communication protocol if the data exchange system is determined to be insecure. Computer system according to Claim 18 , which is included in the data exchange system (100), wherein the data exchange system comprises a quantum circuit system (310, 311, 312) with specific parameters, wherein the quantum circuit system is configured to intercept a qubit on the noisy quantum channel (104), determine the state of the intercepted qubit, and transmit the qubit to the receiver node via the noisy quantum channel; the computer system (105) is configured to use the quantum circuit system to determine the degree of success of an attack; the computer system (105) is configured to determine the degree of reception success using the receiver node (102).

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