A quantum state bidirectional secure transmission method based on quantum encryption

Abstract

The application discloses a quantum state bidirectional secure transmission method based on quantum encryption, constructs a butterfly network model, shares a six-particle maximum entanglement state between a sending node and a control node, performs joint Bell base measurement and two-particle projection measurement on the particles owned by the sending node, performs single-particle measurement on the particles owned by the control node under a measurement base, transmits a classical message to an intermediate node by the sending node, performs coding operation on the received classical message by the intermediate node, transmits the coded result to the next intermediate node, and then transmits the result to two target nodes, performs encryption operation on the respective quantum states by the sending node, transmits the encrypted quantum states to the target nodes, and performs corresponding decryption operation on the encrypted quantum states by the target nodes according to the coding result transmitted by the next intermediate node. The above method combines the ideas of quantum teleportation and remote state preparation, utilizes quantum network coding technology, and realizes perfect cross secure transmission of quantum states in the butterfly network.

Description

Technical Field

[0001] This invention relates to the field of quantum cryptography, and in particular to a method for bidirectional secure transmission of quantum states based on quantum encryption. Background Technology

[0002] Quantum entanglement is a unique resource that has found wide applications in the field of quantum information theory. Quantum teleportation and remote state preparation are two important communication methods. Quantum teleportation (QT) securely transmits an unknown quantum state from one sender to another distant receiver. In QT, the sender possesses the transmitted quantum state but does not know any information about it. Remote state preparation (RSP), on the other hand, can transmit a known quantum state to a receiver at a vast spatial distance. Unlike QT, in RSP, the sender knows the information about the quantum state but does not possess the quantum state to be transmitted. Summary of the Invention

[0003] The purpose of this invention is to provide a quantum state bidirectional secure transmission method based on quantum encryption. This method combines the ideas of quantum teleportation and remote state preparation, and utilizes quantum network coding technology to achieve perfect cross-secure transmission of quantum states in a butterfly network.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A quantum-encrypted bidirectional secure transmission method for quantum states, the method comprising:

[0006] Step 1: Construct a butterfly network model and set up two sending nodes A. i and B i Control node C i Two intermediate nodes D i and D i+1(mod2) Two target nodes A i+1(mod2) and B i+1(mod2) i = 1, 2;

[0007] Step 2, the sending node A i B i With control node C i They share a six-particle maximally entangled state, which serves as a quantum channel for information transmission;

[0008] Step 3, Send to node A i Perform joint Bell basis measurements on the owned particles and send the data to node B. i Perform a two-particle projection measurement on the owned particles and send the measurement results to control node C. i ;

[0009] Step 4, Control Node C i For the particle C i In the measurement base {|l i >,l i A single-particle measurement is performed in {0,1}, and the measurement result is then sent to the sending node A. i B i ;

[0010] Step 5, the sending node A i and B i After receiving the measurement results, classic messages are transmitted respectively. and Give the intermediate node D i ;

[0011] Step 6, the intermediate node D i The received classic message is encoded to obtain the encoded result. The encoded result is then transmitted to the next intermediate node D. i+1(mod2) From the next intermediate node D i+1(mod2) The received encoded result is sent to the two target nodes A. i+1(mod2) and B i+1(mod2) ;

[0012] Step 7, the sending node A i and B i Each quantum state is encrypted, and then the encrypted quantum state is sent to the corresponding target node B. i+1(mod2) and A i+1(mod2) ;

[0013] Step 8, Target Node A i+1(mod2) and B i+1(mod2) According to the next intermediate node D i+1(mod2) The transmitted encoded result is used to perform the corresponding decryption operation on the encrypted quantum state received in step 7 to obtain the target quantum state.

[0014] As can be seen from the technical solution provided by the present invention, the above method combines the ideas of quantum teleportation and long-range state preparation, and uses quantum network coding technology to achieve perfect cross-secure transmission of quantum states in a butterfly network. Attached Figure Description

[0015] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 A schematic diagram of the quantum state bidirectional secure transmission method based on quantum encryption provided in an embodiment of the present invention;

[0017] Figure 2 This is a schematic diagram of the butterfly network constructed in an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments, and do not constitute a limitation of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0019] like Figure 1 The diagram shows a flowchart of a quantum-encrypted bidirectional secure quantum state transmission method according to an embodiment of the present invention. The method includes:

[0020] Step 1: Construct a butterfly network model and set up two sending nodes A. i and B i Control node C i Two intermediate nodes D i and D i+1(mod2) Two target nodes A i+1(mod2) and B i+1(mod2) , i = 1, 2;

[0021] In this step, such as Figure 2 The diagram shown is a schematic of the butterfly network constructed according to an embodiment of the present invention, which includes two sending nodes A. i and B i Control node C i Two intermediate nodes D i and D i+1(mod2) Two target nodes A i+1(mod2) and B i+1(mod2) Long dashed lines represent shared entanglement, solid lines represent classical channels, and short dashed lines represent quantum channels. In the constructed butterfly network model, it is assumed that the unknown quantum state to be transmitted and the known quantum state are respectively... and

[0022] Wherein, parameter γ i and δ i Represents the unknown quantum state to be transmitted The coefficient, parameter λ i and μ i Represents the known quantum state to be transmitted The coefficient of γ; i ,λi and δ i ,μ i Let represent real and complex numbers respectively, and let them satisfy the normalization condition |γ|. i | 2 +|δ i | 2 =1 and |λ i | 2 +|μ i | 2 =1.

[0023] In practice, it utilizes a hybrid communication method combining quantum teleportation and long-range state preparation techniques, simultaneously transmitting both unknown and known quantum states, i.e., A. i →A i+1(mod2) Transmitting unknown quantum states, B i →B i+1(mod2) Transmitting known quantum states.

[0024] Step 2, the sending node A i B i With control node C i They share a six-particle maximally entangled state, which serves as a quantum channel for information transmission;

[0025] In this step, the sending node A i B i With control node C i They share a six-particle maximum entangled state, represented as:

[0026]

[0027] Where |C6> represents the sending node A i B i With control node C i The six-particle maximum entanglement state shared between them;

[0028] Sending node A i Possessing particles (A i,1 A i,2 ), indicating that the sending node A i It possesses 2 particles, where the index i represents the i-th node, i = 1, 2; sending node B i Possessing particles (B i,1 ,B' i,1 B i,2 ), indicating that the sending node B i It has 3 particles, of which B i,1 Represents node B i Possessing particle 1, B' i,1 Represents node B i Possessing particle 2, Bi,2 Represents node B i Possible particles: 3; Control node: C i Possessing particle C i ;

[0029] Therefore, the state of the entire system in the communication network is as follows:

[0030]

[0031] Where |Θ> represents the state of the composite system in the entire communication network, it is represented as The tensor form of and |C6>, where This represents the unknown quantum state to be transmitted.

[0032] Step 3, Send to node A i Perform joint Bell basis measurements on the owned particles and send the data to node B. i Perform a two-particle projection measurement on the owned particles and send the measurement results to control node C. i ;

[0033] In this step, sending node A i For the particles (A) i A i,1 ) at the measurement base The following steps involve performing joint Bell-based measurements, where the Bell measurement basis is as follows:

[0034]

[0035] The superscript i (i = 1, 2) represents the sending node A. i The measurement is performed under the i-th Bell basis; the subscripts 00, 01, 10, and 11 represent two-bit computational bases;

[0036] Meanwhile, sending node B i For the particles (B) i,1 ,B' i,1 In the measurement base The following two-particle projection measurement is performed, with the measurement basis described as follows:

[0037]

[0038] Where the superscript i (i = 1, 2) represents the sending node B. i Perform two-particle projection measurements under the i-th set of measurement bases; λ i It is a real number, μ i It is a complex number, μ i * Represents the complex number μ i Conjugate;

[0039] After measurement, send node A i and B i The measurement results were respectively and With classic message m i n i and s i t i (m i ,n i ,s i ,t i Send to control node C in the form of ∈{0,1}) i ; where the subscript m i n i and s i t i This represents the measurement result, and m i ,n i ,s i ,t i It selects values ​​from the integers 0 and 1;

[0040] Therefore, the entire quantum channel |Θ> can be rewritten as follows:

[0041]

[0042] in, and Indicates two sets of measurement bases; γ i ,δ i and λ i ,μ i Let represent the coefficients of the single-qubit state to be transmitted, and γ i ,λ i and δ i ,μ i They represent real numbers and complex numbers, respectively.

[0043] Step 4, Control Node C i For the particle C i In the measurement base {|l i >,l i A single-particle measurement is performed in {0,1}, and the measurement result is then sent to the sending node A. i B i ;

[0044] In this step, based on the measurement base and The quantum channel |Θ> is re-represented as:

[0045]

[0046] in Indicates sending node Ai Measuring particles (A) i A i,1 The selected Bell measurement base; Represents node B i Measuring particles (B i,1 ,B' i,1 The selected two-particle measurement basis; Indicates control node C i (i = 1, 2) for his particle C i The single-particle measurement basis selected for the measurement, l i The measurement result is represented by a value taken from the integers 0 and 1;

[0047] This indicates that after measurement, the measurement result is m. i ,n i ,s i ,t i ,l i Below, the quantum state formed by the collapse of the quantum system is represented as particle B. i,2 and A i,2 The tensor form, |ψ' i >Represents particle B i,2 state, Represents particle A i,2 state,

[0048] Step 5, the sending node A i and B i After receiving the measurement results, classic messages are transmitted respectively. and Give the intermediate node D i ;

[0049] Step 6, the intermediate node D i The received classic message is encoded to obtain the encoded result. The encoded result is then transmitted to the next intermediate node D. i+1(mod2) ;

[0050] Step 7, the sending node A i and B i Each quantum state is encrypted, and then the encrypted quantum state is sent to the corresponding target node B. i+1(mod2) and A i+1(mod2) ;

[0051] In this step, sending node A i Using the encryption key (m i ,n i ) regarding its own quantum state Perform the encryption operation to obtain the encrypted quantum state. Then the encrypted quantum state is sent to the target node B. i+1(mod2) ;

[0052] in, Indicates encryption operation, m i and n i It belongs to the encryption key; X and Z belong to the quantum Pauli gate, and their matrix representation is as follows: and Acting on a single quantum bit and The process is as follows:

[0053]

[0054]

[0055] Simultaneously send to node B i Using encryption key (s i ,t i ) regarding its own quantum state Perform the encryption operation to obtain the encrypted quantum state. Then the encrypted quantum state is sent to the target node A. i+1(mod2) ;in, Indicates encryption operation; s i and t i It belongs to the encryption key;

[0056] Among them, sending node A i and B i+1(mod2) Shared random key k i Sending node B i and A i+1(mod2) Shared random key r i Then A i and B i Separately, the keys and Send to node B i+1(mod2) and A i+1(mod2) .

[0057] Step 8, Target Node A i+1(mod2) and B i+1(mod2) According to the next intermediate node D i+1(mod2) The transmitted encoded result is used to perform the corresponding decryption operation on the encrypted quantum state received in step 7 to obtain the target quantum state.

[0058] In this step, target node A i+1(mod2) and B i+1(mod2) The decryption operations performed are as follows: and X and Z belong to the quantum Pauli gate; superscript This refers to the decryption key; symbol This represents modulo 2 addition.

[0059] Obtain the target quantum state and The specific process is as follows:

[0060]

[0061]

[0062] Through the above process, it is possible to deterministically achieve perfect cross-secure transmission of four different arbitrary single-qubit states in a quantum butterfly network.

[0063] It is worth noting that the contents not described in detail in the embodiments of the present invention belong to the prior art known to those skilled in the art.

[0064] In summary, the method described in this embodiment of the invention is based on the communication characteristics of quantum teleportation and remote state preparation. The sending node uses the obtained measurement results to encrypt the quantum state and sends the encrypted quantum state to the target node, ensuring that the encrypted information of the quantum state will not be leaked to eavesdroppers during transmission.

[0065] Furthermore, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware, and the corresponding program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk.

[0066] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims. The information disclosed in the background section is intended only to enhance the understanding of the overall background technology of the present invention and should not be construed as an admission or implication in any way that such information constitutes prior art known to those skilled in the art.

Claims

1. A method for bidirectional secure transmission of quantum states based on quantum encryption, characterized in that, The method includes: Step 1: Construct a butterfly network model and set up two sending nodes. and control node Two intermediate nodes and Two target nodes and ; ; Step 2, the sending node , With control node They share a six-particle maximally entangled state, which serves as a quantum channel for information transmission; Step 3, Send Node Perform joint Bell basis measurements on the owned particles and send the node. Perform a two-particle projection measurement on the owned particles and send the measurement results to the control node. ; Step 4, Control Node For the particles possessed in the measurement basis The system performs a single-particle measurement and then sends the measurement result to the transmitting node. , ; Step 5, the sending node and After receiving the measurement results, classic messages are transmitted respectively. and Give the intermediate node ; Step 6, the intermediate node The received classic message is encoded to obtain the encoded result. The encoded result is then transmitted to the next intermediate node. From the next intermediate node Send the received encoded results to the two target nodes. and ; Step 7, the sending node and Each quantum state is encrypted, and then the encrypted quantum state is sent to the corresponding target node. and ; Step 8, Target Node and According to the next intermediate node The transmitted encoded result is used to perform the corresponding decryption operation on the encrypted quantum state received in step 7 to obtain the target quantum state.

2. The quantum-encrypted bidirectional secure transmission method for quantum states according to claim 1, characterized in that, In the butterfly network model constructed in step 1, the unknown quantum state to be transmitted and the known quantum state are respectively and ; Among them, parameters and Represents the unknown quantum state to be transmitted coefficients; parameters and Represents the known quantum state to be transmitted The coefficient; and Let represent real numbers and complex numbers respectively, and let them satisfy the normalization condition. and .

3. The quantum-encryption-based bidirectional secure transmission method for quantum states according to claim 2, characterized in that, In step 2, the sending node , With control node They share a six-particle maximum entangled state, represented as: ； in, Indicates the sending node , With control node The six-particle maximum entanglement state shared between them; Sending node Possessing particles , indicating the sending node It has 2 particles, where the subscript Indicates the first 1 node Sending node Possessing particles , indicating the sending node It has 3 particles, of which Represents a node Possessing 1 particle Represents a node Possessing 2 particles, Represents a node Possible Particles 3; Control Node Possessing particles ; Therefore, the state of the entire system in the communication network is as follows: ； in, It represents the state of the composite system in the entire communication network, and is expressed as: and The tensor form, in which This represents the unknown quantum state to be transmitted.

4. The quantum-encrypted bidirectional secure transmission method for quantum states according to claim 3, characterized in that, In step 3, the sending node For particles and In measurement base The following steps involve performing joint Bell-based measurements, where the Bell measurement basis is as follows: ； superscript Indicates the sending node exist Measurements are performed under the Bell basis; subscripts 00, 01, 10, and 11 indicate two-bit computational basis. Meanwhile, sending node For the particles possessed In measurement base The following two-particle projection measurement is performed, with the measurement basis described as follows: ； Among them, superscript Indicates the sending node exist Two-particle projection measurements were performed under the group measurement basis. It is a real number. It is a plural number. Representing complex numbers Conjugate; After measurement, the sending node and The measurement results were respectively and With classic news and Send to the control node in the form of ; where subscript and Indicates the measurement result, and It selects values ​​from the integers 0 and 1; Thus the entire quantum channel It can be rewritten: ； in, and Indicates two sets of measurement bases; and Let represent the coefficients of the single-qubit state to be transmitted, and . and They represent real numbers and complex numbers, respectively.

5. The quantum-encryption-based bidirectional secure transmission method for quantum states according to claim 4, characterized in that, In step 4, based on the measurement base , and Quantum Channel Represented as: ； in Indicates the sending node Measuring particles Selected Bell measurement base; Represents a node Measuring particles The selected two-particle measurement basis; Indicates control node His particles The single-particle measurement basis selected for the measurement was... The measurement result is represented by a value taken from the integers 0 and 1; This indicates that after measurement, the measurement result is... Below, the quantum state formed by the collapse of a quantum system is represented as a particle. and tensor form, Represents particles state, Represents particles state, .

6. The quantum-encrypted bidirectional secure transmission method for quantum states according to claim 5, characterized in that, In step 7, the sending node Using encryption keys Regarding its own quantum state Perform the encryption operation to obtain the encrypted quantum state. Then, the encrypted quantum state is sent to the target node. ; in, Indicates an encryption operation. and It belongs to the encryption key; X and Z Belonging to the quantum Pauli gate, their matrix representation is as follows: and Acting on a single quantum bit and The process is as follows: ； ； Simultaneously sending nodes Using encryption keys Regarding its own quantum state Perform the encryption operation to obtain the encrypted quantum state. Then, the encrypted quantum state is sent to the target node. ;in, Indicates an encryption operation; and It belongs to the encryption key; Among them, the sending node and Share a pair of random keys Sending node and Share a pair of random keys ;Then and Separately, the keys and Send to node and .

7. The quantum-encrypted bidirectional secure transmission method for quantum states according to claim 6, characterized in that, In step 8, the target node and The decryption operations performed are as follows: and ; in, X and Z Belongs to the quantum Pauli gate; superscript , , , This refers to the decryption key; symbol This represents modulo 2 addition. Obtain the target quantum state and The specific process is as follows: ； 。

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