CN110086547B - An Optimal Controlled Quantum Teleportation Method for Arbitrary Unknown n-Particles with Adjustable Threshold - Google Patents

Abstract

The invention discloses an optimal controlled quantum invisible state transfer method for any unknown n particles with adjustable threshold values. The inventionA threshold value adjustable arbitrary unknown n particle optimal controlled quantum invisible state transfer method is characterized by comprising the following steps: the central service node prepares corresponding entangled state, and distributes corresponding entangled particles to Alice and Bob of both communication parties through quantum channels, and three control groups C₁、C₂、C₃Any one member of (a); three control groups C₁、C₂、C₃The other members of the system take particles sent by the central service node as control quanta and take |0>And executing the C-NOT operation as the target quantum bit to generate the control particle. The invention has the beneficial effects that: 1. according to the optimal controlled quantum invisible transmission method for any unknown n particles with the adjustable threshold value, the safety and flexibility of information transmission are realized by the optimal controlled method with the adjustable threshold value.

Description

An Optimal Controlled Quantum Teleportation Method for Arbitrary Unknown n-Particles with Adjustable Threshold

technical field

The invention relates to the field of quantum, in particular to an optimal controlled quantum teleportation method for any unknown n-particle with adjustable threshold value.

Background technique

Quantum information and quantum computing are emerging interdisciplinary disciplines based on the principles of quantum mechanics, classical information science and classical computing science. Due to the superposition, unclonability and uncertainty of quantum states, quantum communication has the unique advantages of large communication capacity and high security, and can be widely used in military, national defense and information security and other fields. Among them, thanks to the continuous updating and improvement of various branch protocols such as quantum secure direct communication, quantum dialogue, and quantum key distribution, quantum communication products with practical value have gradually been applied.

Since Bennett et al. proposed quantum teleportation in 1993 [1], this technology has been regarded as one of the important foundations for realizing quantum communication. Unlike ultra-dense coding that uses shared entanglement and quantum channels to transmit classical information, quantum teleportation uses shared entanglement, local operations and classical communication to teleport an unknown quantum state to a distant receiver. In quantum teleportation, Alice and Bob share a bell state |ψ> _AB as a quantum channel. First, Alice measures the bell state between the particle to be transmitted and the particle A she owns, and sends the measurement result to Bob through the classical channel. . After Bob obtains Alice's measurement result, he performs the corresponding unitary transformation on the particle B he owns to restore the original state of the particle to be transmitted. Using the principle of quantum teleportation can complete the process of information transmission and information processing between the two communicating parties, and the repeater of the quantum communication network should be constructed by relying on the principle of quantum teleportation.

The traditional technology has the following technical problems:

Research on quantum teleportation has been very active in recent years. In 2015, the progress of quantum teleportation was summarized by Pirandola [2] et al., who reviewed the basic theoretical ideas of quantum teleportation and its different protocols. By focusing on the main experiments, as well as the technical advantages and disadvantages of various techniques, it concludes with a discussion of open issues, challenges, and possible future implementations. In 2017, Ren [3] et al. conducted quantum teleportation experiments with the ground through Micius, showing that the quantum teleportation of independent single-photon quantum states from ground observatories to low-Earth orbit satellites, through uplink channels, distances up to 1400 km. Due to the existence of photon loss, the distance of quantum teleportation using fiber channel or terrestrial free space channel is about 100 kilometers.

At the same time, researches on multi-level quantum systems [4], multi-bit quantum teleportation systems [5-9] and controllable quantum teleportation systems [8-12] have also produced a lot of excellent results. In 2015, Zhang, B. et al. proposed a three-bit quantum state teleportation scheme based on four-bit entangled states, which pointed out that four-bit entangled states can be used, and an auxiliary bit and a c-Not operation can be introduced simultaneously to achieve three-bit quantum state teleportation. Teleportation of bit quantum states [7]. In 2016, Verma [11] et al. explicitly proposed standard quantum teleportation and controlled quantum teleportation protocols, and analyzed the situation of complete teleportation using general quantum channels and measurement bases. At the same time, Xu [12] et al. proposed a controlled quantum teleportation protocol, in which quantum information in an unknown state is trusted by the sender (Alice) through GHZ entangled particles under the control of the controller Charlie. sent to the remote receiver (Bob). Research on controlled quantum teleportation usually involves a fixed number of controllers, which limits the usability and flexibility of the protocol, and if some controllers sometimes fail to provide services, the entire protocol cannot be realized.

[1] C.H.Bennett,G.Brassard,et al.Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.Phys.Rev.Lett.,1993,70(13)

[2] Pirandola S., Eisert J., Weedbrook C., et al. Advances in quantumteleportation. Nature Photonics, 2015, 9(10):5439-5439.

[3] Ren J.G., Xu P., Yong H.L., et al. Ground-to-satellite quantumteleportation. Nature, 2017, 549(7670):70-73

[4] S.K.Goyal, P.E.Boukama-Dzoussi, S.Ghosh, et al., "Qudit-Teleportation for photons with linear optics", Nature Scientific Reports, 2014, 4(13):4543

[5] Li, YH., Li, XL., Nie, LP., et al., “Quantum Teleportation of Three and Four-Qubit State Using Multi-qubit Cluster States”, International Journal of Theoretical Physics, 2016, 55(3) :1820-1823

[6] Li, Z., Long, LR., Zhou, P., et al., “Probabilistic multiparty-controlled teleportation of an arbitrary m-qubit state with a pure entangled quantum channel against collective noise”, Science China Physics Mechanics&Astronomy, 2012 , 55(12):2445-2451

[7] Zhang, B., Liu, X., Wang, J., et al., “Quantum Teleportation of a Three-qubit State using a Four-qubit Entangled State”, International Conference on Computer, 2015, 53(12) :4079-4082

[8] Wang, JW., Shu, L., Mo, ZW., et al., “Controlled Teleportation of a QuditState by Partially Entangled GHZ States”, International Journal of Theoretical Physics, 2014, 53(8):2867-2873

[9] Zhou, P., Li, XH., Deng, FG., et al., “Multiparty-controlled teleportation of an arbitrary m-qudit state with pure entangled quantum channel”, Journal of Physics A Mathematical&Theoretical, 2012, 40(43 ):13121-13130

[10] Cao H.J., Yu Y.F., Song Q., et al.A Quantum Proxy Weak BlindSignature Scheme Based on Controlled Quantum Teleportation. International Journal of Theoretical Physics, 2015, 54(4): 1325-1333

[11] Verma V., Prakash H., Standard Quantum Teleportation and Controlled Quantum Teleportation of an Arbitrary N-Qubit Information State. International Journal of Theoretical Physics, 2016, 55(4): 2061-2070

[12] Xu X., Wang X., Controlled Quantum Teleportation via the GHZEntangled Ions in the Ion-Trapped System. International Journal of Theoretical Physics, 2016, 55(8):3551-3554.

SUMMARY OF THE INVENTION

为了实现通信的安全性和灵活性，我们引入三个控制组，每组可以有任意多个成员。在量子信道的确定过程中，每组可以任意选取成员进行单粒子测量，并公布测量结果。控制成员越多越能够满足灵活性的要求，因为此时个别成员出现无法提供服务的情况依然不会影响到整个通信过程。方案中所涉及到的技术有大量的理论和实验基础，所以是切实可行的。另外，协议所设计的bell态测量和单粒子测量，以及四种酉操作都是具有实用性和可行性的，所以我们的方案是简单易行的。The technical problem to be solved by the present invention is to provide an optimal controlled quantum teleportation method for any unknown n particle with adjustable threshold value. In this protocol, we use the principle of quantum teleportation to construct an adjustable threshold value. The optimal controlled quantum teleportation construction scheme of arbitrary unknown n-particles, Alice and Bob transmit an unknown quantum state

In order to achieve the security and flexibility of communication, we introduce three control groups, each group can have any number of members. In the process of determining the quantum channel, each group can arbitrarily select members to perform single-particle measurements and publish the measurement results. The more control members, the more flexible it is, because the failure of individual members to provide services at this time will not affect the entire communication process. The technology involved in the scheme has a large theoretical and experimental basis, so it is practical. In addition, the bell state measurement and single-particle measurement, as well as the four unitary operations designed in the protocol are practical and feasible, so our scheme is simple and easy to implement.

In order to solve the above technical problems, the present invention provides an optimal controlled quantum teleportation method for any unknown n-particle with adjustable threshold value, including:

The central service node prepares the corresponding entangled state, and distributes the corresponding particles to Alice and Bob, both communicating parties, and any member of the three control groups C ₁ , C ₂ , and C ₃ ;

The central service node prepares corresponding entangled states, including two bell states and entangled states GHZ states and W states required by the controller. The two bell states, GHZ states and W states have the following forms:

Then the overall state of the system can be expressed as follows:

It can be seen from the above formula that particles A and B form a bell state |ψ _i > _AB (i=0,1).

It is assumed that the particle to be transmitted is a single particle: |ψ _n >=α|0>+β|1>, where α and β are complex numbers and satisfy |α| ² +|β| ² =1. Then the whole system state can be written as:

It can be concluded from the above formula that the following table exists between the measurement results of the controller, Alice's measurement results and the unitary operations that Bob needs to perform:

The number of members of the three control groups C ₁ , C ₂ , and C ₃ can be dynamically changed according to actual business requirements, and the states of particles held by all members in each control group are the same. The particle distribution of the central service node is completed through the quantum channel.

The other members of the three control groups C ₁ , C ₂ , C ₃ use the particles sent by the central service node as control qubits, and use |0> as the target qubit to perform C-NOT operation to generate control particles; the C-NOT operation It has such a characteristic: when the control qubit is |0>, the target qubit state remains unchanged; when the control qubit state is |1>, the target qubit state is flipped. This ensures that all members of each group have control particles in the same state.

The three control groups C ₁ , C ₂ , C ₃ can be composed of any number of members, and it must be pointed out that the reliability of the system will increase with the increase of the number of members, because the control group composed of multiple members can allow Some members were disconnected. Therefore, each of the three control groups selects at least one member from its group that performs single-bit measurements on the control particles it possesses.

The three control groups select any member from their group, and this member performs single-bit measurements on the control particles it owns. At the same time, Alice performs bell measurements on the particle n and particle A to be transmitted, and publishes their respective data through the classical channel. Measurement results; if the measurement results are the same, then it is proved that their control state is the GHZ state, and if they are not exactly the same, it is proved to be the W state.

The Alice performs bell measurement on the particle n to be transmitted and the particle A, and the obtained measurement result |ψ _i > _nA is in the form of four bell states: |ψ _i > _nA (i=0,1,2,3). in,

According to the measurement result of the controller and Alice's measurement result, Bob performs the corresponding unitary transformation on the particle B, thereby restoring the state of the particle n to be transmitted. The unitary transformation has the following form:

By establishing multiple channels, Alice can convert a quantum state consisting of n unknown particles

隐形传送到Bob。

Teleport to Bob.

Beneficial effects of the present invention:

传输过程中，要引入三个控制组，每组可以有任意多个成员。在量子信道的确定过程中，每组可以任意选取成员执行单粒子测量，并公布测量结果。控制成员越多越能够满足灵活性的要求，因为此时个别成员出现无法提供服务的情况依然不会影响到整个通信过程。1. An optimal controlled quantum teleportation method for any unknown n-particles with adjustable threshold value of the present invention realizes the security and flexibility of information transmission by the optimal controlled method with adjustable threshold value, so in the unknown state to be transmitted

During transmission, three control groups are introduced, and each group can have any number of members. During the determination of the quantum channel, each group can arbitrarily select members to perform single-particle measurements and publish the measurement results. The more control members, the more flexible it is, because the failure of individual members to provide services at this time will not affect the entire communication process.

2. An optimal controlled quantum teleportation method for any unknown n-particles with adjustable threshold value of the present invention, since the bell state quantum channel is finally established between the source node Alice and the destination node Bob, the entire process requires Single-event measurements, bell-based measurements, classical communication, and four local operations are all achievable, and the protocol itself is simple and easy to use.

3. An optimal controlled quantum teleportation method for any unknown n-particles with adjustable threshold value of the present invention, the number of people in the control group is dynamically adjustable, so whether it is applied in scenarios with high or low security requirements , the scheme can produce the optimal control results. Secondly, the control process does not require all control members to participate in it at the same time, which avoids the situation that the entire communication process cannot be completed when individual members cannot provide services, thereby improving the flexibility of solution implementation.

Description of drawings

Fig. 1 is a flow chart of the optimal controlled quantum teleportation method for any unknown n-particles with adjustable threshold value of the present invention.

FIG. 2 is a schematic diagram of the distribution of particles to source node Alice, destination node Bob and three control groups by the central service node in the optimal controlled quantum teleportation method for arbitrary unknown n particles with adjustable threshold value of the present invention.

Fig. 3 shows the transmission of source node Alice teleportation particle n after the Bell channel is established between source node Alice and destination node Bob in the optimal controlled quantum teleportation method of arbitrary unknown n particles with adjustable threshold value of the present invention Schematic.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

的隐形传递过程。两个控制组中部分成员对自己所拥有的粒子进行单粒子测量，并向Alice和Bob公布测量结果。Alice与Bob能够解析出二者之间的具体量子信道的形式，从而促使信息的高效、安全传输。The main realization idea of the present invention is: in a quantum communication system, the source node Alice and the destination node Bob determine the form of the quantum channel between them with the assistance of the control group to complete the unknown quantum state

the invisible transmission process. Some members of the two control groups perform single-particle measurements on the particles they own, and publish the measurement results to Alice and Bob. Alice and Bob can parse out the form of the specific quantum channel between them, thus promoting the efficient and secure transmission of information.

Referring to Figure 2, an optimal controlled quantum teleportation method for any unknown n-particle with adjustable threshold value of the present invention, the specific implementation steps of the method are as follows:

Step 1. The central service node prepares the corresponding entangled state, and distributes the corresponding particles to Alice and Bob, both communicating parties, and any member of the three control groups C ₁ , C ₂ , and C ₃ ;

The central service node prepares corresponding entangled states, including two bell states and entangled states GHZ states and W states required by the controller. Two of the bell states have the following forms:

Then the overall state of the system can be expressed as follows:

It can be seen from the above formula that particles A and B form a bell state |ψ _i > _AB (i=0,1).

It is assumed that the particle to be transmitted is a single particle: |ψ _n >=α|0>+β|1>, where α and β are complex numbers and satisfy |α| ² +|β| ² =1. Then the whole system state can be written as:

It can be concluded from the above formula that the following table exists between the measurement results of the controller, Alice's measurement results and the unitary operations that Bob needs to perform:

The number of members of the three control groups C ₁ , C ₂ , and C ₃ can be dynamically changed according to actual business requirements, and the states of particles held by all members in each control group are the same. The particle distribution of the central service node is completed through the quantum channel.

Step 2. The other members of the three control groups C ₁ , C ₂ , and C ₃ use the particles sent by the central service node as control qubits, and use |0> as the target qubit to perform C-NOT operation to generate control particles;

The other members of the three control groups C ₁ , C ₂ , C ₃ use the particles sent by the central service node as control qubits, and use |0> as the target qubit to perform C-NOT operation to generate control particles; where C- The NOT operation has such a characteristic: when the state of the control qubit is |0>, the state of the target qubit remains unchanged; when the state of the control qubit is |1>, the state of the target qubit is flipped. This ensures that all members of each group have control particles in the same state.

The three control groups C ₁ , C ₂ , C ₃ can be composed of any number of members, and it must be pointed out that the reliability of the system will increase with the increase of the number of members, because the control group composed of multiple members can allow Some members were disconnected. Therefore, each of the three control groups selects at least one member from its group that performs single-bit measurements on the control particles it possesses.

Step 3. The three control groups select any member from their group, and the member performs single-bit measurement on the control particles it owns. At the same time, Alice performs bell measurement on the particle n and particle A to be transmitted, and announces it through the classical channel. their respective measurements;

The three control groups select any member from their group respectively, and this member performs single-bit measurement on the control particles it owns. If the measurement results are the same, it proves that their control state is the GHZ state, if not the same, It is proved to be the W state.

The Alice performs bell measurement on the particle n to be transmitted and the particle A, and the obtained measurement result |ψ> _nA is in the form of four bell states: | _ψi > _nA (i=0,1,2,3). in,

隐形传送到Bob。Step 4: Bob performs a corresponding unitary transformation on particle B according to the measurement result of the controller and the measurement result of Alice, so as to restore the state of the particle n to be transmitted. By establishing multiple channels, Alice can convert a quantum state composed of n unknown particles

Teleport to Bob.

The Bob performs the corresponding unitary transformation on the particle B according to the measurement result of the controller and the measurement result of Alice, where the unitary transformation has the following form:

的任意一个粒子，经过n条路径的隐形传送，Alice可以将未知量子态

隐形传送给Bob。The particle to be transmitted n is a quantum state

Any particle of , through teleportation of n paths, Alice can transfer the unknown quantum state

Teleport to Bob.

A specific application scenario of the present invention is introduced below:

的传输举例说明，其中α，β为复数，且满足|α|²+|β|²＝1。in quantum state

, where α and β are complex numbers and satisfy |α| ² +|β| ² =1.

Step 1. The central service node prepares the corresponding entangled state, and distributes the corresponding particles to Alice and Bob, both communicating parties, and any member of the three control groups C ₁ , C ₂ , and C ₃ ;

The central service node prepares corresponding entangled states, including two bell states and entangled states GHZ states and W states required by the controller. The two bell states, GHZ states and W states have the following forms:

Then the overall entangled state of the system can be expressed as:

It can be seen from the above formula that particles A and B form a bell state |ψ _i > _AB (i=0,1).

Assuming that the particle to be transmitted is a single particle: |ψ _n >=α|0>+β|1>, the entire system state can be written as:

It can be concluded from the above formula that the following table exists between the measurement results of the controller, Alice's measurement results and the unitary operations that Bob needs to perform:

那么Bob在得知Alice的测量态为|ψ₁>_nA的情况下，他只需要对自己的粒子B执行幺正操作U₂就可以将粒子B的状态从Assuming that the measurement results of the controllers are exactly the same, it can be inferred that the shared quantum entanglement state between them is

Then, when Bob knows that Alice's measurement state is |ψ ₁ > _nA , he only needs to perform the unitary operation U ₂ on his particle B to change the state of particle B from

恢复为待传送粒子n的原始状态：

Return to the original state of the particle n to be transported:

If there is an n-particle quantum state, only n teleportation paths need to be established to complete the entire teleportation process.

An optimal controlled quantum teleportation method for any unknown n particles with adjustable threshold of the present invention completes the unknown quantum state between two terminal nodes under the implementation of the optimal controlled scheme with adjustable threshold. Teleportation, it should be noted, introduces three control groups, each of which can have any number of members. During the determination of the quantum channel, each group can arbitrarily select members to perform single-particle measurements and publish the measurement results. The more control members, the more flexible it is, because the failure of individual members to provide services at this time will not affect the entire communication process.

The above-mentioned embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention is subject to the claims.

Claims (1)

1. A threshold value adjustable arbitrary unknown n particle optimal controlled quantum invisible state transfer method is characterized by comprising the following steps:

the central service node prepares corresponding entangled states and distributes corresponding particles to Alice and Bob of both communication parties and three control groups C₁、C₂、C₃Any one member of (a);

the central service node prepares corresponding entangled states, including two bell states and an entangled state GHZ state and a W state required by a controller; wherein the two bell states, GHZ state and W state have the following forms:

the overall state of the system can be expressed as follows:

from the above equation, it can be seen that the particles A, B form the bell state | ψ_i>_ABWherein i is 0, 1;

assume that the particle to be transferred is a single particle: phi_n>＝α|0>+β|1>Wherein α, β are complex numbers and satisfy | α! α -²+|β|²1 is ═ 1; the entire system can be written as:

from the above equation, the following table can be summarized between the measurement result of the controller, the measurement result of Alice, and the unitary operation that Bob needs to perform:

the three control groups C₁、C₂、C₃The number of members of (a) may vary dynamically according to actual business requirements, and the quantum states of the particles held by all members in each control group are the same; the particle distribution of the central service node is completed through a quantum channel;

three control groups C₁、C₂、C₃The other members of the system take particles sent by the central service node as control quanta and take |0>Performing C-NOT operation as a target quantum bit to generate a control particle; wherein the C-NOT operation has the following characteristics: when the control qubit is |0>Time, target amountThe sub-bit state remains unchanged; when the control qubit is |1>Then, the target qubit state is flipped; this ensures that all members in each group have control particles in the same state;

the three control groups C₁、C₂、C₃Can be composed of any number of members, and it must be pointed out that the reliability of the system will increase with the increase of the number of members, because the control group composed of a plurality of members can allow some members to be dropped; so in three control groups, each group selects at least one member from its group, and the member carries out single-bit measurement on the control particles owned by the member;

selecting any member from the three control groups respectively, and performing single-bit measurement on the control particles owned by the member; if the measurement results of the three groups are the same, the control state of the three groups is proved to be the GHZ state, and if the measurement results are not completely the same, the control state is proved to be the W state; simultaneously, Alice carries out bell measurement on the particles n and A to be transmitted, and publishes respective measurement results thereof through a classical channel; measurement result | ψ of Alice>_nAIn the form of four bell states: phi_i>_nA(i ═ 0,1,2, 3); wherein,

bob executes corresponding unitary transformation on the particle B according to the measurement results of the three control groups and the measurement result of Alice, so as to recover the state of the particle n to be transmitted; wherein the unitary transform has the form:

by establishing multiple channels, Alice can convert a quantum state consisting of n unknown particles

Stealth is delivered to Bob.

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