KR102128362B1 - Method of synchronzing qunatum network and quantum system performing thereof - Google Patents

Abstract

A method for synchronizing a quantum network according to the present invention is provided. The method comprises: a frequency synchronization configuration step of performing a clock network configuration for frequency synchronization by using a quantum clock synchronized with a second device as a receiving device; And an asynchronous detection step of detecting desynchronization due to frequency drift in the clock network, and using multiple degrees of freedom (DOF) of a single photon in a quantum network (QN), It can improve the accuracy of clock synchronization.

Description

A quantum network synchronization method and a quantum system performing the same{Method of synchronzing qunatum network and quantum system performing thereof}

The present invention relates to a quantum network synchronization method and a quantum system performing the same. More particularly, it relates to a method and system for synchronizing quantum hyperentangled quantum clocks.

In quantum clock synchronization, a protocol for using a previous entanglement for synchronized clock generation has been proposed by Josza et al., but a protocol for efficient transmission of the quantum clock needs to be presented. Giovannetti et al. relate to quantum clock synchronization and mention how to use quantum effects for positioning.

On the other hand, in quantum clock synchronization, synchronization is the core of timekeeping applications where the clock of a spatially distributed network is required to provide accurate information. Navigation, localization and telecommunications are applications that directly benefit from this clock synchronization. With the advent of accurate clocks so far, the need for accurate clock synchronization is very important. On the other hand, 3.2 × 10 ^- The optical clock based on ¹⁷¹ Yb + has a relative uncertainty of the system ¹⁸ has been provided. These optical watches are based on the discovery of various physics phenomena such as gravitational wavelengths. Beyond the classical technique, the special theory of relativity provides a procedure for the synchronization of distributed clocks, known as Einstein synchronization, related to the operational line of sight exchange of light pulses between two systems.

Meanwhile, in the procedure for synchronizing the optical clock of the network, the entangled state of the network can be used to provide ultra-precision information about the deviation of the local oscillator (LO). These deviations must be accurately calculated to Heisenberg precision using quantum effects.

However, according to what has been known so far, in the case of realistic evolution models, at the node affected by fluctuations in the frequency of the LO, frequency asynchronousity is detected through mutual measurement of various factors, etc. There is a problem that a protocol for a method of performing synchronization has not been proposed.

Accordingly, an object to be solved in the present invention is to provide an accurate quantum network synchronization method through mutual measurement of various factors, etc. in a node affected by fluctuation of the frequency of LO.

In addition, an object to be solved in the present invention is to provide a method for detecting frequency asynchronousity and performing frequency resynchronization through mutual measurement of various factors.

A quantum network synchronization method according to the present invention for solving the above problems is provided. The method comprises: a frequency synchronization configuration step of performing a clock network configuration for frequency synchronization by using a quantum clock synchronized with a second device as a receiving device; And an asynchronous detection step of detecting desynchronization due to frequency drift in the clock network, and using multiple degrees of freedom (DOF) of a single photon in a quantum network (QN), It can improve the accuracy of clock synchronization.

In an embodiment, a frequency resynchronization step of performing frequency resynchronization through phase estimation may be further included.

In an embodiment, in the frequency synchronization configuration step, information on the state of N singlets shared between the first device and the second device may be obtained. In this case, the singlet state may be changed by introducing a sinusoidal component having a bell-based to the singlet state.

In one embodiment, the asynchronous detection step performs a bell state measurement for a photon, and provides information on polarization degrees of freedom (POL DOF) for the photon based on the measurement of the bell state. Transmitting to the 2 devices, it is possible to receive the results of the mutual measurement (joint measurement) for the POL DOF from the second device. In this case, if the frequency deviation due to the frequency drift exceeds the allowable range associated with the asynchronous detection based on the mutual measurement result, the frequency resynchronization step may be performed.

에 의한 유니터리

를 이용하여 변화(evolution)시킬 수 있다. 이때, 상기 변화에 의한 SPA DOF의 변화는 주파수 드리프트 파라미터(χ)에 의해 결정될 수 있다. 또한, 상기 주파수 드리프트 파라미터(χ)에 관한 확률 분포를 통해 상기 위상 예측을 수행하고, 상기 위상 예측에 기반하여 상기 주파수 재동기화를 수행할 수 있다.In one embodiment, in the frequency resynchronization step, photons in a hyperentangled state

By unity

It can be changed using (evolution). At this time, the change in SPA DOF due to the change may be determined by the frequency drift parameter (χ). Further, the phase prediction may be performed through a probability distribution of the frequency drift parameter (χ), and the frequency resynchronization may be performed based on the phase prediction.

Provided is a quantum transmission device that performs a quantum network synchronization method according to another aspect of the present invention. The quantum transmitting device includes: an interface unit configured to receive information on a synchronized quantum clock from a second device that is a receiving device; And a control unit configured to perform a clock network configuration for frequency synchronization using the synchronized quantum clock, and to detect desynchronization due to frequency drift in the clock network.

In one embodiment, the control unit may perform frequency resynchronization through phase estimation.

In one embodiment, the control unit may acquire information regarding the state of N singlets shared between the first and second devices, which are the quantum transmission devices. Further, the singlet state may be changed by introducing a sine wave component having a bell basis to the singlet state.

In one embodiment, the control unit performs a bell state measurement for a photon, and based on the measurement of the bell state, information about polarization degrees of freedom (POL DOF) for the photon to the second device It can be controlled to transmit. In addition, the second device may be controlled to receive a result of a joint measurement for the POL DOF. In addition, if the frequency deviation due to the frequency drift exceeds the allowable range associated with the asynchronous detection based on the mutual measurement result, the clock reference of the clock network may be resynchronized.

에 의한 유니터리

를 이용하여 변화(evolution)시킬 수 있다. 이때, 상기 변화에 의한 SPA DOF의 변화는 주파수 드리프트 파라미터(χ)에 의해 결정될 수 있다. 또한, 상기 주파수 드리프트 파라미터(χ)에 관한 확률 분포를 통해 상기 위상 예측을 수행하고, 상기 위상 예측에 기반하여 상기 주파수 재동기화를 수행할 수 있다. In one embodiment, the controller, the photon of the hyperentangled state (hyperentangled state)

By unity

It can be changed using (evolution). At this time, the change in SPA DOF due to the change may be determined by the frequency drift parameter (χ). Further, the phase prediction may be performed through a probability distribution of the frequency drift parameter (χ), and the frequency resynchronization may be performed based on the phase prediction.

A method of synchronizing a quantum network according to another aspect of the present invention is provided. The method comprises: a frequency synchronization configuration step of performing a clock network configuration for frequency synchronization with a first device as a transmitting device by transmitting information about a synchronized quantum clock performed by a second device as a receiving device; And an asynchronous prediction step of detecting a frequency drift of a clock qubit in the clock network to predict desynchronization.

In an embodiment, a frequency resynchronization step of performing frequency resynchronization through phase estimation may be further included.

In an embodiment, in the frequency synchronization configuration step, information on the state of N singlets shared between the first device and the second device may be obtained. In this case, the singlet state may be changed by introducing a sinusoidal component having a bell-based to the singlet state.

In one embodiment, in the asynchronous prediction step, information on polarization degrees of freedom (POL DOF) for a photon based on a bell state measurement for a photon is received from the first device, and the POL Results of joint measurement for DOF can be obtained. Also, the frequency resynchronization step may be performed when the frequency deviation due to the frequency drift exceeds an allowable range associated with the asynchronous prediction based on the mutual measurement result.

에 의한 유니터리

를 이용하여 변화(evolution)시킬 수 있다. 이때, 상기 변화에 의한 SPA DOF의 변화는 주파수 드리프트 파라미터(χ)에 의해 결정될 수 있다. 또한, 상기 주파수 드리프트 파라미터(χ)에 관한 확률 분포를 통해 상기 위상 예측을 수행하고, 상기 위상 예측에 기반하여 상기 주파수 재동기화를 수행할 수 있다.In one embodiment, the frequency resynchronization step, the photon of the hyperentangled state (hyperentangled state)

By unity

It can be changed using (evolution). At this time, the change in SPA DOF due to the change may be determined by the frequency drift parameter (χ). Further, the phase prediction may be performed through a probability distribution of the frequency drift parameter (χ), and the frequency resynchronization may be performed based on the phase prediction.

A quantum receiving device for performing a quantum network synchronization method according to another aspect of the present invention is provided. The quantum receiving device is an interface unit configured to transmit information on a synchronized quantum clock to a first device that is a transmitting device, a clock network for frequency synchronization of the first device using the synchronized quantum clock Perform configuration ―; And a control unit configured to detect frequency drift of a clock qubit in the clock network and predict desynchronization.

In one embodiment, the control unit may perform frequency resynchronization through phase estimation.

In one embodiment, the control unit may acquire information on the state of N singlets shared between the first device and the second device. Further, the singlet state may be changed by introducing a sine wave component having a bell-based basis to the singlet state.

In one embodiment, the control unit receives information on polarization degrees of freedom (POL DOF) for photons based on a Bell state measurement for photons from the first device, and for the POL DOF Joint measurement results can be obtained. In addition, the frequency re-synchronization may be performed when the frequency deviation due to the frequency drift exceeds an allowable range associated with the asynchronous prediction based on the result of the mutual measurement.

에 의한 유니터리

를 이용하여 변화(evolution)시킬 수 있다. 이때, 상기 변화에 의한 SPA DOF의 변화는 주파수 드리프트 파라미터(χ)에 의해 결정될 수 있다. 또한, 상기 주파수 드리프트 파라미터(χ)에 관한 확률 분포를 통해 상기 위상 예측을 수행하고, 상기 위상 예측에 기반하여 상기 주파수 재동기화를 수행할 수 있다.In one embodiment, the controller, the photon of the hyperentangled state (hyperentangled state)

By unity

It can be changed using (evolution). At this time, the change in SPA DOF due to the change may be determined by the frequency drift parameter (χ). Further, the phase prediction may be performed through a probability distribution of the frequency drift parameter (χ), and the frequency resynchronization may be performed based on the phase prediction.

According to at least one embodiment of the present invention, by using multiple degrees of freedom (DOF) of a single photon in a quantum network (QN), there is an advantage of improving the accuracy of quantum clock synchronization.

In addition, according to at least one embodiment of the present invention, by achieving the ultimate quantum resource limit in clock synchronization, there is an advantage that can realize the quantum network by removing other obstacles of the quantum Internet.

1 shows a quantum system for performing quantum network synchronization according to the present invention.
2 shows a detailed configuration of a quantum device according to the present invention.
3 shows the architecture of a clock network according to the present invention.
4 shows the probability Pb representing the similarity of the changed state according to the deviation according to the present invention.
5 is a conceptual diagram showing a frequency shift effect in a singlet state according to the present invention.
Figure 6 shows the quantum transmission of the POL of the N-Qubit from Alice side to Bob side according to the present invention.
7 shows a conceptual diagram for interferometric analogy of frequency shift prediction according to the present invention.
8 is a flowchart of a quantum network synchronization method performed by a first device, which is a transmission device according to the present invention.
9 is a flowchart of a quantum network synchronization method performed by a second device that is a receiving device according to the present invention.

The above-described features and effects of the present invention will become more apparent through the following detailed description in connection with the accompanying drawings, and accordingly, those skilled in the art to which the present invention pertains can easily implement the technical spirit of the present invention. Will be able to. The present invention can be applied to various changes and may have various forms, and specific embodiments will be illustrated in the drawings and described in detail in the text. However, it is not intended to limit the present invention to a specific disclosure form, it should be understood to include all modifications, equivalents, or substitutes included in the spirit and scope of the present invention. The terminology used herein is only used to describe specific embodiments and is not intended to limit the present invention.

In describing each drawing, similar reference numerals are used for similar components.

Terms such as first and second may be used to describe various components, but the components should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from other components.

For example, the first component may be referred to as a second component without departing from the scope of the present invention, and similarly, the second component may be referred to as a first component. The term “and/or” includes a combination of a plurality of related described items or any of a plurality of related described items.

Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by a person skilled in the art to which the present invention pertains.

Terms such as those defined in a commonly used dictionary should be interpreted as having meanings consistent with meanings in the context of related technologies, and should not be interpreted as ideal or excessively formal meanings unless explicitly defined in the present application. Should not.

The suffixes "modules", "blocks" and "parts" for the components used in the following description are given or mixed in consideration of only the ease of writing the specification, and do not have meanings or roles distinguished from each other by themselves. .

Hereinafter, with reference to the accompanying drawings, preferred embodiments of the present invention will be described so that those skilled in the art can easily carry out. In the following description of embodiments of the present invention, when it is determined that detailed descriptions of related well-known functions or well-known configurations may unnecessarily obscure the subject matter of the present invention, detailed descriptions thereof will be omitted.

Hereinafter, a quantum network synchronization method according to the present invention and a quantum system performing the same will be described.

In this regard, FIG. 1 shows a quantum system for performing quantum network synchronization according to the present invention. As illustrated in FIG. 1, the quantum system includes a plurality of subsystems, and for convenience, the first subsystem 100 and the second subsystem 200 may be expressed as being included. However, the present invention is not limited to the first and second sub-systems 100 and 200, and may be applied to any number of sub-systems. Meanwhile, the first to third sub-systems 100 and 200 may be any quantum device. In this regard, the first and second subsystems 100 and 200 may be first (quantum) devices that are transmitting devices and second (quantum) devices that are receiving devices, respectively. On the other hand, the first (quantum) device 100 and the second (quantum) device 200, if any one device is a transmitting device, the other device may be a receiving device. Meanwhile, the case where the first (quantum) device 100 is a control station (or a base station, a server) that controls a plurality of second (quantum) devices 200 is also included.

2 shows a detailed configuration of a quantum device according to the present invention. For convenience, the transmitting device may be referred to as the first device 100 and the receiving device may be referred to as the second device 200. However, the present invention is not limited thereto, and vice versa, as described above, can also operate simultaneously as a transmitting/receiving device. Meanwhile, the third device 300 may be a device that mediates and/or controls quantum communication between the first device 100 and the second device 200.

The first device 100 includes a control unit 110, an interface unit 120, and a memory 130. Similarly, the second device 200 also includes a control unit 210, an interface unit 220, and a memory 230. Here, since the interface units 120 and 220 transmit and receive quantum data through a quantum channel, it may be referred to as a quantum interface unit. In addition, since the interface units 120 and 220 may transmit and receive some control data or related information through a classic channel, it may also be referred to as a general interface unit. That is, the interface units 120 and 220 may include physically separated quantum interface units and general interface units, or logically divided quantum interface units and general interface units.

Referring to FIG. 2, a detailed operation of the transmitting device 100 performing the quantum network synchronization method according to the present invention will be described as follows. In this regard, quantum network synchronization may be performed by the transmitting device 100 or the receiving device 200. In addition, quantum network synchronization may be performed by the quantum server 500 of FIG. 1 based on information from the transmitting device 100 or the receiving device 200. Hereinafter, for convenience, it will be described as being performed by the transmitting device 100 or the receiving device 200, but is not limited thereto, and is performed by other entities such as the quantum server 500 is also included in the scope of the present invention.

The interface unit 120 is configured to receive information about a synchronized quantum clock from a second device that is a receiving device. Meanwhile, the control unit 110 is configured to perform a clock network configuration for frequency synchronization using the synchronized quantum clock. In this regard, the control unit 110 may perform the following operations for frequency synchronization. That is, the control unit 110 obtains information on the state of N singlets shared between the first device and the second device. In addition, the controller 110 may change the singlet state by introducing a sinusoidal component of a bell basis to the singlet state.

In addition, the control unit 110 is configured to detect desynchronization due to frequency drift in the clock network. In this regard, the controller 110 may perform the following operations for asynchronous detection. That is, the control unit 110 performs a bell state measurement for a photon and transmits information on polarization degrees of freedom (POL DOF) for the photon to the second device based on the measurement of the bell state. Can be controlled. Also, the control unit 110 may control to receive a result of a joint measurement of the POL DOF from the second device.

에 의한 유니터리

를 이용하여 변화(evolution)시킬 수 있다. 이때, 상기 변화에 의한 SPA DOF의 변화는 주파수 드리프트 파라미터(χ)에 의해 결정될 수 있다. 이에 따라, 제어부(110)는 상기 주파수 드리프트 파라미터(χ)에 관한 확률 분포를 통해 상기 위상 예측을 수행하고, 상기 위상 예측에 기반하여 상기 주파수 재동기화를 수행할 수 있다.Meanwhile, the control unit 110 may perform frequency resynchronization through phase estimation. In this regard, the controller 110 resynchronizes the clock reference of the clock network when the frequency deviation due to the frequency drift exceeds an allowable range associated with the asynchronous detection based on the mutual measurement result. Can. Specifically, the control unit 110 photons in the hyperentangled state

By unity

It can be changed using (evolution). At this time, the change in SPA DOF due to the change may be determined by the frequency drift parameter (χ). Accordingly, the controller 110 may perform the phase prediction through the probability distribution of the frequency drift parameter (χ), and perform the frequency resynchronization based on the phase prediction.

Meanwhile, the memory 130 is configured to store quantum information or general information in relation to quantum network synchronization.

Meanwhile, referring to FIG. 2, a detailed operation of the receiving device 100 performing the quantum network synchronization method according to the present invention will be described as follows. In this regard, as described above, the transmitting device 100 may perform quantum network synchronization, but is performed by the receiving device 200, or the transmitting device 100 and the receiving device 200 are cooperated. It is also possible.

The interface unit 220 is configured to transmit information about a synchronized quantum clock to a first device that is a transmitting device. At this time, the first device may perform a clock network configuration for frequency synchronization using the synchronized quantum clock.

Meanwhile, the following operations may be performed in relation to performing the quantum synchronization based on the receiving device. In this regard, the control unit 210 may obtain information regarding the state of N singlets shared between the first device and the second device. In addition, the controller 210 may change the singlet state by introducing a sinusoidal component of a bell basis to the singlet state.

Meanwhile, the control unit 210 may be configured to detect frequency drift of a clock qubit in the clock network to predict desynchronization. In this regard, the controller 210 may control to receive information on polarization degrees of freedom (POL DOF) for a photon based on a bell state measurement for the photon from the first device. In addition, the control unit 210 may obtain a joint measurement result for the POL DOF. In this case, if the frequency deviation due to the frequency drift exceeds the allowable range associated with the asynchronous prediction based on the mutual measurement result, the frequency resynchronization may be performed.

에 의한 유니터리

를 이용하여 변화(evolution)시킬 수 있다. 이때, 상기 변화에 의한 SPA DOF의 변화는 주파수 드리프트 파라미터(χ)에 의해 결정될 수 있다. 또한, 제어부(210)는 상기 주파수 드리프트 파라미터(χ)에 관한 확률 분포를 통해 상기 위상 예측을 수행하고, 상기 위상 예측에 기반하여 상기 주파수 재동기화를 수행할 수 있다.Meanwhile, the controller 210 may perform frequency resynchronization through phase estimation. Specifically, the controller 210 photons in a hyperentangled state

By unity

It can be changed using (evolution). At this time, the change in SPA DOF due to the change may be determined by the frequency drift parameter (χ). In addition, the control unit 210 may perform the phase prediction through probability distribution of the frequency drift parameter (χ), and perform the frequency resynchronization based on the phase prediction.

On the other hand, with respect to the quantum network synchronization method according to the present invention, look at the preliminaries (preliminaries) as follows. The natural change of the quantum system is dominated by the natural state of the quantum system. For the qubit, |0> represents the lower energy eigen state E ₁ , while |1> represents the high excited state E ₂ . This type of natural hamiltonian is expressed by Equation 1 below.

로 표현된다. 따라서, 에너지 고유 상태의 큐빗(|0>,|1>)은 비-변화(non-evolving)하지만, 두 개의 상태의 중첩으로 존재한다면, 이는 자연적 hamiltonian M 하에서 변화한다. 하지만, 얽힘 상태, 예컨대 싱글릿(|ψ′>)은 자신의 변화에 대한 각각의 로컬 입자에 대해 작용하는 hamiltonian에 달려있다. 자연적 hamiltonian은 예를 들어 수학식 2와 같은 외부(external) hamiltonian으로 대체될 수 있다.The unity change for this hamiltonian

It is expressed as Thus, the cubits (|0>,|1>) in the energy-intrinsic state are non-evolving, but if they exist as a superposition of two states, they change under natural hamiltonian M. However, the entangled state, eg singlet (|ψ′>), depends on the hamiltonian acting on each local particle for its change. Natural hamiltonian can be replaced with an external hamiltonian, for example, in Equation 2.

Here, Ω is the Rabi frequency of Rabi flopping between states. In this way, the present invention can control changes in the quantum system. To replace the natural hamiltonian with the outer hamiltonian H, a rotating frame picture cancels out the inner hamiltonian M can be used. The rotating frame creates a unity that corresponds to the unitary change produced by the natural hamiltonian. The rotation frame must affect the system by generating a unitary change represented by R that cancels U ₀ (t) as shown in Equation 3 below.

Considering the total hamiltonian (natural + external) = M+H, in the present invention, it is possible to obtain a rotating frame hamiltonian by solving an equation such as Equation 4 below.

Under the internal and external hamiltonian, considering the time derivative of the current state corresponding to the changing state, and using the derivative law of multiplication, the following Equation 5 can be obtained.

This leads to Hr = R(t)HR ^† (t), which counteracts the effect of internal hamiltonian. Thus, the underlying quantum system now only changes under the external hamiltonian H.

Frequency Synchronization Network Configuration

The creation of hyperentangled states is as follows. In this regard, Figure 3 shows the architecture of a clock network according to the invention. Each clock has a qubit that changes under a hamiltonian like Equation 3. Along the clock, super-entanglement of POL and SPA DOF is utilized for asynchronous detection and parameter prediction. The n singlet state of the super-entangled photon's POL DOF changes under the same Hamiltonian as a clock qubit. These singlets form the basis of the frequency drift detection block. After the clock asynchronous is detected, the hyperentangled state plays a role in Heisenberg limit parameter prediction.

On the other hand, looking at the creation of the super-entangled state according to the present invention. In this regard, a pair of orthogonally oriented type-II phase matched β-Barium Borate crystals can be pumped to receive two low energy photons entangled with POL DOF. By simply selecting the j =±1 orbital angular momentum (OAM) mode, a photon state entangled with POL and spatial DOF can be generated as shown in Equation 6 below.

Therefore, the singlet of the POL DOF will be used for the resynchronization protocol, while the state of Equation 6 will form the basis of parameter prediction. If the two spatially spaced particles are under the same unitary evolution, the singlet state does not change. One of these scenarios is a unity defined by hamiltonian H as in Equation 3. For this hamiltonian, the laser pulse maintained during t = π /Ω duration is derived by Equation 7 below.

However, this is generally not the case if binary quantum systems are not singlets. 3 shows another network configuration according to the present invention. The network uses multiple degrees of freedom (DOF) associated with photons. Polarization (POL) DOF includes a quantum clock, while Orbital Angular Momentum (POL) DOF is a state of N singlet shared between two targets (eg Alice and Bob) for asynchronous detection. Includes. The quantum systems of the two DOFs are made to change simultaneously under the same unity. For the purpose of this protocol, the present invention considers that both sides' clot qubits change under hamiltonian as in Equation 8.

Where χ is the frequency drift at the original frequency Ω. For χ=1, this hamiltonian has the form of Equation 2. Therefore, in the absence of Rabi frequency drift, the singlet of the POL DOF will not change. As soon as the lag/leadχ of the Rabi frequency is present in the local laser, the unitary change for the qubit in the target is as shown in Equation 9 below.

On the other hand, Figure 4 shows the probability P _b showing the similarity of the changed state according to the deviation (deviation) according to the present invention. Here, the probability P _b represents the similarity of the changed state using the singlet state through the dot product. The blue curve represents the decrease in probability P _b while experiencing local frequency lag/lead χ. For χ = 1.1, the probability P _b represented by the red dot and line corresponds to the total deviation under unitary change. Here, the unitary change of two singlet states for χ = 1.1 has the same probability effect as the single change under χ = 0.2.

Regarding the frequency drift, considering the frequency drift χ in which Alice has a total frequency Ω′ = χ Ω, this change is expressed by changing the singlet state by introducing a bell-based sinusoidal component as shown in Equation 10 below. It is possible.

The laser pulse induced change at t = t ₂ leads to the state of Equation 11 below.

Now, instead of the frequency drift χ, it is possible to consider the drift 2χ which leads to the state as in Equation 12 below.

Detection of desynchronization

In order to detect and predict the asynchronousness of the clock network due to frequency drift, the present invention contemplates a positive-operator valued measure (POVM) that meets one of the core objectives of this protocol. That is, the same POVM not only provides an optimal measurement method for predicting frequency drift with Heisenberg scaling, but can also be used for synchronization detection.

For this purpose, in the present invention, a POVM based on a projective measurement given as Equation 13 below may be considered.

The set of measurement vectors given above that satisfy the valid POVM conditions have the following characteristics:

-The measurement operator obtained as A _i =|μ _i ><μ _i | is Hermitian and is positive semi-defnite.

-∑ _i A _i = I H.

To apply the joint meaurement POVM of Equation 12, Alice's POL DOF can be teleported to all states to the Bob side device. To this end, the SPA DOF can be used in the present invention. Assuming EPR shared by SPA, it has the form of Equation 14 below.

By using the bell state measurement on the Alice side device and transmitting a 2-bit general result for each qubit, a state as in Equation 15 below can be achieved.

In order to obtain the overall state of the POL DOF, in the present invention, the bobbit of the SPA DOF can be swapped using the dummy qubit of the POL DOF of the secondary photon in the Bob side device as shown in Equation 16 below.

By applying the exchange operation, the result as shown in Equation 17 below can be obtained.

This derives all qubits for the combined measurement of POL DOF in the state as in Equation 18.

This particular POVM not only acts as a basis for providing Heisenberg scaled parameter prediction, but also provides the same probability distribution for equations 10 and 11.

Therefore, for the POVM of Equation 12, n'subsequent application of U'ⓧ U with drift χ with respect to the state of Equation 9, n subsequent applications) provides the same probability distribution as a single unitary application with drift nχ. Will induce This drift will induce a singlet state change, unlike the case of U ⓧ U, which guides in detecting asynchronousness.

Once the POL DOF is no longer a singlet, in the present invention, the clock reference needs to be resynchronized if the deviation exceeds the allowable interval for asynchronous detection as in Figure 4 at the time of measurement. If not, in the present invention, despite implementing a series of POVMs performed with unitary application, it waits until subsequent application of U'ⓧ U leads to a state beyond an allowable interval. The allowable interval for frequency shift is bounded by the changeable state and achievable probability for precise discrimination between singlets. In the absence of asynchronous, the present invention has a non-changing singlet state. With respect to any POVM application for measurement, the singlet state will always have the same probability distribution. For the measurement vector |μi> in the singlet state, the associated probability is expressed as Equation 19 below, which is always 1 for the singlet state because the other measurement vectors are orthogonal thereto.

However, if the N singlet of the POL DOF of all parties starts to change by frequency drift, the probability distribution of two successive measurements of t = t ₁ and t = t ₂ for a given POVM will be different.

The probability of obtaining a specific measurement result is presented to be proportional to the number of times that the associated post measurement state is obtained. As an example, the present invention considers the case of a frequency drop by 3/4 of the original frequency expressed by χ = 0.75. In addition, two ensembles of N bipartite states in the form of Equations 9 and 10 are considered at t = t ₁ and t = t ₂ , respectively. Using POVM, |ψ _t1 >_|μ1> = 0.8536 and |ψ _t2 > _| You can get a result of _{μ1 >} = 0.5. This allows the probability to drop after a subsequent change under U′ⓧ U for a singlet state, and a given POVM is used to detect the frequency drift.

를 유도한다.On the other hand, Figure 5 is a conceptual diagram showing the frequency shift effect in a singlet state according to the present invention. The frequency shift on the Alice side induces a change in the singlet state under the unitary U'ⓧ U. The upper bound deviation limit is set by the frequency cut-off, and the change in the singlet state is the state.

Induces

On the other hand, Figure 6 shows the quantum transmission of the POL of the N-Qubit from Alice side to Bob side according to the present invention.

Frequency Resynchronization via Phase Estimation

In order to predict the network asynchronous due to frequency drift, the present invention considers a positive-operator valued measure (POVM) that satisfies one of the core objectives of this protocol; In other words, it provides an optimal measurement method for predicting frequency drift with Heisenberg scaling. For this kind of measurement operator, the classical Fisher information (CFI) is the same as the quantum Fisher information (QFI). Using the upper bound as in Equation 20 below, general Fisher information relates to the variance of the predicted drift χ.

For the probe state of n copies, the quantum bound obtained for the optimal measurement operator is expressed by Equation 21 below.

Here, the inequality sign is due to the additive property of the quantum Fisher information F. However, using the quantum advantage associated with the singlet state, the quantum Fisher information can be scaled to the square of the number of copies of the used prote state. This advantage leads to Heisenberg scaling. Here, in the case of maximum entanglement between N parties, the variation of parameter prediction is scaled (limited) as in Equation 22 below.

Quantum Fisher information for this case can be obtained, where the probe state is a pure spin singlet and is expressed as Equation 23 below.

Local measurements of spin-1/2 bell states provide shot noise with limited scaling instead of Heisenberg. Therefore, the present invention requires a combined measurement to achieve maximum accuracy. The advantage of distinguishing resynchronization from asynchronous detection and parameter prediction is that all 2n particles can be used for parameter prediction (because all particles in the singlet experience the unity encoding the parameters). Accordingly, for a single 2-cubit state, the maximum Fisher information increases to F _max = 4.

In the present invention, the probe singlet state and unitary operation U" ⓧ U" are considered in a typical metrology scenario as shown in FIG. 7. That is, FIG. 7 shows a conceptual diagram for interferometric analogy of frequency shift prediction according to the present invention. The hamiltonian H expressed in equation (2) is related to the frequency drift χ as the linear change in σ _x.

Referring to FIG. 7, a measurement method discussed in the present invention may perform measurement using POVM of Equation (12). The idea itself is based on the idea that a system entangled with the environment under a U-shaped open system change provides details of weak measurements related to a entangled quantum system with a measurement setup that can exist with different photon degrees of freedom. .

The resulting state is tracked by measurements of the quantum system DOF, achieving a probability distribution that provides general Fisher information equal to its quantum Fisher information. The extension of this idea corresponds to the interaction between hyperentangled DOFs, where the POL DOF controls the change in the state of the SPA DOF. All photons in the super-entangled state can exist on the Alice side using multiple DOF quantum transmissions and change under the unitary change U" ⓧ U" as shown in Equation 24 below.

Here, H'is measurable for POL DOF, while x is measurable for SPA DOF. g is the coupling strength of the two DOFs, while H'contains the information of the frequency drift χ, and t = π/Ω denotes the total duration that the two DOFs interact.

을 이용하여 SPA DOF의 결과 상태로부터 확률 분포를 획득할 수 있다. 이러한 확률 분포의 파라미터 χ에 대한 미분(derivative)은

의 관계를 통해 QFI를 찾는데 도움이 되고, 본 발명에서 이 값은 16σ²이 된다. 두 개의 DOF 간에 상호작용의 세기 g의 알려진 값에 대하여, 본 발명에서 제시된 상한 관계를 이용하여 관련된 입자의 수의 제곱에 따른 파라미터의 변화를 예측할 수 있다. The result of Equation 24 is the hybrid entangled state and the change in SPA DOF is dominated by the parameter χ. Finally, the measurement for the POL DOF portion of the resulting state is measured using POVM in Equation (12). Through POVM, in the present invention

Probability distribution can be obtained from the result state of SPA DOF using. The derivative of the probability distribution for the parameter χ is

It helps to find the QFI through the relationship of, and in the present invention, this value is 16σ ² . For a known value of the intensity g of the interaction between two DOFs, the upper bound relationship presented in the present invention can be used to predict the change in parameter with the square of the number of particles involved.

On the other hand, the present invention provides an interferometric implementation of hyperentanglement assisted metrology. To this end, in the present invention, a bell state is used together with particles having the same polarization in a spatially entangled state having a POL DOF and a Gaussian distribution.

Looking at the results and effects of the present invention are as follows. In the present invention, hyperentangled bipartite states were used for both detection and prediction scenarios. This scenario has an advantage over local multipartite entanglement because it is easier to prepare and less sensitive to noise. The measurement setup used for asynchronous detection is important because the decent approach for parameter prediction uses the same POVM to predict frequency drift with Heisenberg scaling.

This protocol relies on the consumption of super-entangled resources and general information available for regular probing of the clock network. Ultra-entangled precision frequency Control can be combined with weak measurements to achieve closed loop clock asynchronous detection and resynchronization systems, and achieve clock accuracy and stability in quantum networks.

In the above, the quantum devices performing the quantum network synchronization method according to the present invention and the principles thereof have been described in detail. Hereinafter, a quantum network synchronization method according to another aspect of the present invention will be described.

In this regard, FIG. 8 shows a flowchart of a quantum network synchronization method performed by a first device that is a transmitting device according to the present invention. On the other hand, Figure 9 shows a flow diagram of a quantum network synchronization method performed by a second device that is a receiving device according to the present invention.

Referring to FIG. 8, a method for synchronizing quantum networks performed by a first device that is a transmitting device includes a frequency synchronization configuration step (S110), an asynchronous detection step (S120), and a frequency resynchronization step (S130).

In the frequency synchronization configuration step (S110), a clock network configuration for frequency synchronization is performed by using a synchronized quantum clock synchronized with a second device that is a receiving device.

In addition, in the asynchronous detection step (S120 ), desynchronization due to frequency drift is detected in the clock network. Specifically, in the asynchronous detection step (S120 ), information regarding the state of N singlets shared between the first device and the second device is obtained. In this case, the singlet state may be changed by introducing a sinusoidal component having a bell-based to the singlet state.

Meanwhile, in the asynchronous detection step (S120 ), a bell state measurement on the photon may be performed. In addition, information on polarization degree of freedom (POL DOF) for photons may be transmitted to the second device based on the measurement of the bell state. In addition, a result of a joint measurement for the POL DOF may be received from the second device. Meanwhile, if the frequency deviation due to the frequency drift exceeds the allowable range associated with the asynchronous detection based on the mutual measurement result, a frequency resynchronization step (S130) may be performed.

에 의한 유니터리

를 이용하여 변화(evolution)시킬 수 있다. 이때, 상기 변화에 의한 SPA DOF의 변화는 주파수 드리프트 파라미터(χ)에 의해 결정될 수 있다. 이때, 상기 주파수 드리프트 파라미터(χ)에 관한 확률 분포를 통해 상기 위상 예측을 수행하고, 상기 위상 예측에 기반하여 상기 주파수 재동기화를 수행할 수 있다.Correspondingly, in the frequency resynchronization step (S130), frequency resynchronization is performed through phase estimation. Specifically, in the frequency resynchronization step (S130), photons in a hyperentangled state

By unity

It can be changed using (evolution). At this time, the change in SPA DOF due to the change may be determined by the frequency drift parameter (χ). In this case, the phase prediction may be performed through a probability distribution of the frequency drift parameter (χ), and the frequency resynchronization may be performed based on the phase prediction.

Referring to FIG. 9, a method for synchronizing quantum networks performed by a second device that is a receiving device includes a frequency synchronization configuration step (S210), an asynchronous detection step (S220), and a frequency resynchronization step (S230).

In the frequency synchronization configuration step (S210 ), information on a synchronized quantum clock is transmitted to configure a clock network for frequency synchronization with a first device that is a transmitting device. Specifically, in the frequency synchronization configuration step (S210 ), information regarding the state of N singlets shared between the first device and the second device may be obtained. Further, the singlet state may be changed by introducing a sine wave component having a bell-based basis to the singlet state.

Meanwhile, in the asynchronous detection step (S220 ), frequency drift of a clock qubit is detected in the clock network to predict desynchronization. Specifically, in the asynchronous detection step (S220 ), information on polarization degrees of freedom (POL DOF) for a photon based on a bell state measurement for a photon may be received from the first device. In addition, it is possible to obtain a result of the joint measurement (joint measurement) for the POL DOF. In addition, a frequency resynchronization step (S230) may be performed when the frequency deviation due to the frequency drift exceeds an allowable range associated with the asynchronous prediction based on the result of the mutual measurement.

에 의한 유니터리

를 이용하여 변화(evolution)시킬 수 있다. 이때, 상기 변화에 의한 SPA DOF의 변화는 주파수 드리프트 파라미터(χ)에 의해 결정될 수 있다. 또한, 상기 주파수 드리프트 파라미터(χ)에 관한 확률 분포를 통해 상기 위상 예측을 수행하고, 상기 위상 예측에 기반하여 상기 주파수 재동기화를 수행할 수 있다.On the other hand, in the frequency resynchronization step (S230), the photon of the hyperentangled state (hyperentangled state)

By unity

It can be changed using (evolution). At this time, the change in SPA DOF due to the change may be determined by the frequency drift parameter (χ). Further, the phase prediction may be performed through a probability distribution of the frequency drift parameter (χ), and the frequency resynchronization may be performed based on the phase prediction.

In the above, the quantum system and the quantum network synchronization method for performing the quantum network synchronization method according to the present invention have been described. Looking at the effect and application field and technology commercialization prospects according to the present invention are as follows.

According to at least one embodiment of the present invention, by using multiple degrees of freedom (DOF) of a single photon in a quantum network (QN), there is an advantage that the accuracy of quantum clock synchronization can be improved.

In addition, according to at least one embodiment of the present invention, by achieving the ultimate quantum resource limit in clock synchronization, there is an advantage that can realize the quantum network by removing other obstacles of the quantum Internet.

The field of application of the present invention is the field of quantum computers and communication using quantum networks, and in this field requires very accurate synchronization between distributed nodes so that the network operates properly.

With regard to the technology commercialization prospects of the present invention, it can be used to establish a quantum cryptographic communication link. In this regard, a hyperentangled quantum communication system (QCS) improves the synchronization accuracy of clocks at network nodes, enabling faster communication.

According to the software implementation, each component may be implemented as a separate software module as well as the procedures and functions described herein. Each of the software modules may perform one or more functions and operations described herein. Software code can be implemented in a software application written in an appropriate programming language. The software code is stored in a memory and can be executed by a controller or processor.

100: first subsystem 200: second subsystem
300: quantum server
110, 210: control unit 120, 220: interface unit
130, 230: memory

Claims (20)

In the quantum network synchronization method, the method is performed by a first device that is a transmitting device,
A frequency synchronization configuration step of performing a clock network configuration for frequency synchronization by using a synchronized quantum clock synchronized with a second device that is a receiving device;
An asynchronous detection step of detecting desynchronization due to frequency drift in the clock network; And
And a frequency resynchronization step of performing frequency resynchronization through phase estimation,
The asynchronous detection step,
Bell state measurement for photons is performed,
Transmits information on polarization degrees of freedom (POL DOF) for photons to the second device based on the measurement of the bell state,
Receiving a joint measurement (joint measurement) results for the POL DOF from the second device,
Performing the frequency resynchronization step when the frequency deviation due to the frequency drift exceeds an allowable range associated with the asynchronous detection based on the mutual measurement result,
The frequency resynchronization step,
Photons in hyperentangled state

By unity

Evolution using, where H′ is measurable for POL DOF, x is measurable for SPA DOF, g is the coupling strength of two DOFs, and H′ is frequency drift χ Information, and t = π /Ω denotes the total duration of interaction between two DOFs ―
The change in SPA DOF due to the change is determined by the frequency drift parameter (χ),
A method for synchronizing quantum networks, wherein the phase prediction is performed through a probability distribution of the frequency drift parameter (χ) and the frequency resynchronization is performed based on the phase prediction. delete According to claim 1,
The frequency synchronization configuration step,
Acquire information about the N singlet (singlet) state shared between the first device and the second device,
A method for synchronizing quantum networks by introducing a sinusoidal component of a bell basis on the singlet state to evolve the singlet state. delete delete In the quantum transmission device for performing a quantum network synchronization method,
An interface unit configured to receive information on a synchronized quantum clock from a second device that is a receiving device; And
A controller configured to perform clock network configuration for frequency synchronization using the synchronized quantum clock, and to detect desynchronization due to frequency drift in the clock network,
The control unit,
Bell state measurement for photons is performed,
Based on the measurement of the bell state, control to transmit information about the polarization degree of freedom (POL DOF) for the photon to the second device,
Control to receive the result of the joint measurement (joint measurement) for the POL DOF from the second device,
Resynchronizing the clock reference of the clock network when the frequency deviation due to the frequency drift exceeds the allowable range associated with the asynchronous detection based on the mutual measurement result,
Photons in hyperentangled state

By unity

Evolution using-where H'is measurable for POL DOF, x is measurable for SPA DOF, g is the coupling strength of two DOFs, and H'is the frequency drift of χ Information, t = π /Ω indicates the total duration that the two DOFs interact with,
The change in SPA DOF due to the change is determined by the frequency drift parameter (χ),
A quantum transmission device that performs phase prediction through probability distribution on the frequency drift parameter (χ) and performs frequency resynchronization based on the phase prediction. The method of claim 6,
The control unit,
A quantum transmission device that performs frequency resynchronization through phase estimation. The method of claim 6,
The control unit,
Acquire information about the N singlet (singlet) state shared between the first device and the second device that is the quantum transmission device,
A quantum transmission device that introduces a bell-based sinusoidal component into the singlet state to evolve the singlet state. delete delete In the quantum network synchronization method, the method is performed by a second device that is a receiving device,
A frequency synchronization configuration step of transmitting information on a synchronized quantum clock to perform clock network configuration for frequency synchronization with a first device as a transmitting device;
An asynchronous prediction step of detecting a frequency drift of a clock qubit in the clock network to predict desynchronization; And
And a frequency resynchronization step of performing frequency resynchronization through phase estimation,
The asynchronous prediction step,
Receiving information about polarization degrees of freedom (POL DOF) for photons based on Bell state measurement for photons from the first device,
Acquire the joint measurement (joint measurement) results for the POL DOF,
When the frequency deviation due to the frequency drift exceeds the allowable range associated with the asynchronous prediction based on the mutual measurement result, the frequency resynchronization step is performed,
The frequency resynchronization step,
Photons in hyperentangled state

By unity

Evolution using-where H'is measurable for POL DOF, x is measurable for SPA DOF, g is the coupling strength of two DOFs, and H'is the frequency drift of χ Information, t = π /Ω indicates the total duration that the two DOFs interact with,
The change in SPA DOF due to the change is determined by the frequency drift parameter (χ),
A method for synchronizing quantum networks, wherein the phase prediction is performed through a probability distribution of the frequency drift parameter (χ) and the frequency resynchronization is performed based on the phase prediction. delete The method of claim 11,
In the frequency synchronization configuration step,
Acquire information about the N singlet (singlet) state shared between the first device and the second device,
A method for synchronizing quantum networks by introducing a sinusoidal component of a bell basis on the singlet state to evolve the singlet state. delete delete In the quantum receiving device performing a quantum network synchronization method,
An interface unit configured to transmit information on a synchronized quantum clock to a first device as a transmitting device, wherein the first device performs clock network configuration for frequency synchronization using the synchronized quantum clock; And
And a control unit configured to detect frequency drift of a clock qubit in the clock network and predict desynchronization,
The control unit,
Frequency resynchronization is performed through phase estimation,
The control unit,
Receiving information about polarization degrees of freedom (POL DOF) for photons based on Bell state measurement for photons from the first device,
Acquire the joint measurement (joint measurement) results for the POL DOF,
When the frequency deviation due to the frequency drift exceeds the allowable range associated with the asynchronous prediction based on the mutual measurement result, the frequency resynchronization is performed,
Photon in hyperentangled state

By unity

Evolution using-where H'is measurable for POL DOF, x is measurable for SPA DOF, g is the coupling strength of two DOFs, and H'is the frequency drift of χ Information, t = π /Ω indicates the total duration that the two DOFs interact with,
The change in SPA DOF due to the change is determined by the frequency drift parameter (χ),
A quantum receiving device that performs the phase prediction through a probability distribution of the frequency drift parameter (χ) and performs the frequency resynchronization based on the phase prediction. delete The method of claim 16,
The control unit,
Acquiring information about the N singlet (singlet) state shared between the first device and the second device,
A quantum receiving device that introduces a bell-based sinusoidal component into the singlet state to evolve the singlet state. delete delete

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