Quantum secure direct communication method based on one-time pad mode

Abstract

The application discloses a kind of quantum secure direct communication methods based on one-time one secret mode, belong to quantum communication technical field, including the following steps: Bob prepares a batch of coherent state and sends to Alice through quantum channel, Alice will received coherent state be divided into two groups, to one group is executed homodyne detection, and detection result is sent to Bob, and Bob carries out safety detection according to the first effective information quantity;Alice encodes coherent state according to secret information, and sends to Bob after encoding, Bob randomly selects one coherent state and executes homodyne detection, and result is sent to Alice, and Alice carries out safety detection according to the second effective information quantity;Bob executes homodyne detection to the rest of coherent state and calculates threshold value, and demodulation is obtained secret information;The application uses continuous variable quantum state, easy to produce and detect, small in transmission process loss, high security, can be compatible with standard telecommunication technology.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of quantum communication, and particularly relates to a quantum secure direct communication method based on one-time pad mode. BACKGROUND

[0002] In classical secure communication, one-time pad is the only absolutely secure classical encryption mode in theory so far. In classical one-time pad, since the keys used for encryption and decryption by the two communication parties are completely random for eavesdroppers, and the keys are used only once, the ciphertext transmitted in the channel, i.e. the file obtained by encrypting the secret information with the key, is completely random for the eavesdroppers; that is, the secret information obtained by the eavesdroppers from the ciphertext has the same effect as directly guessing the secret information, and thus the absolute security of the classical one-time pad is actually based on the complete randomness of the key.

[0003] Quantum secure direct communication is a new branch of quantum communication, and is different from quantum key distribution in that the secret message of the sender is directly transmitted to the receiver in quantum secure direct communication without sharing a private key in advance. In other words, quantum secure direct communication has no ciphertext, no key, and even no key management. Only a protocol meeting the following two requirements can be called quantum secure direct communication: on the one hand, after the transmission of the quantum bit, the receiver should directly read out the secret information without additional classical information; on the other hand, the encoded quantum state should not be leaked even if there is an eavesdropper present, that is, the eavesdropper cannot obtain any useful information in the quantum state.

[0004] At present, most quantum secure direct communication protocols are based on single-photon discrete variable states for communication, however, single photons are difficult to be compatible with standard telecommunication technology, and are not easy to generate and detect, and are prone to encounter large loss in the transmission process, and the communication efficiency is low. SUMMARY

[0005] The present application aims to provide a quantum secure direct communication method based on one-time pad mode, so as to solve the problem of low communication efficiency of the existing quantum secure direct communication.

[0006] To solve the above technical problems, the technical solution adopted by the present application is a quantum secure direct communication method based on one-time pad mode, comprising the following steps:

[0007] S1, the sender prepares a set of coherent states A, and transmits them to the receiver through a quantum channel;

[0008] S2. The receiver randomly divides the received coherent state A into coherent state S and coherent state B, performs homodyne detection on each coherent state in the coherent state S, and sends the orthogonal position, orthogonal momentum and homodyne detection result of the coherent state S to the sender. The sender performs a security check based on the first effective information amount. If the first effective information amount is greater than the security threshold, the sender proceeds to the next step. If the first effective information amount is less than the security threshold, the sender abandons the communication.

[0009] S3. The receiver encodes the coherent state B according to the secret information. If the secret information sent is 0, the unitary operation D(α1) is used for encoding. If the secret information sent is 1, the unitary operation D(α2) is selected for encoding and the encoded coherent state B is sent to the sender.

[0010] S4. The sender randomly selects a coherent state from the received coherent state B to perform homodyne detection, and sends the orthogonal position, orthogonal momentum and homodyne detection result of the coherent state to the receiver. The receiver performs a security check based on the second effective information amount. If the second effective information amount is greater than the security threshold, the receiver proceeds to the next step. If the second effective information amount is less than the security threshold, the receiver abandons the communication.

[0011] S5. The sender performs homodyne detection on the remaining coherent states B and calculates the threshold. If the homodyne detection result is less than the threshold, the sender believes that the receiver is performing the unitary operation D(α1) and demodulates to obtain the secret information 0. If the homodyne detection result is greater than the threshold, the sender believes that the receiver is performing the unitary operation D(α2) and demodulates to obtain the secret information 1.

[0012] S6. After demodulation is completed, the sender calculates the quantum bit error rate of the secret information 0 and 1, and determines whether the quantum channel is secure based on the quantum bit error rate.

[0013] Furthermore, in step S1, the coherent state A received by the receiver is represented by |X A +iP A >, where:

[0014]

[0015] Where, X A is the orthogonal position of the coherent state received by the receiver, P A is the orthogonal momentum of the coherent state received by the receiver, X B is the orthogonal position of the coherent state sent by the sender, P B is the orthogonal momentum of the coherent state sent by the sender, i is the imaginary unit, δX ex Represents X A The channel noise, δP ex Indicates P A The channel noise, δX vRepresents X A Shot noise, δP v Indicates P A The shot noise, ∈ is the excess noise during transmission, T is the transmission efficiency, T = 10 -0.02L , L is the transmission distance, V B is the modulation variance of the sender.

[0016] Furthermore, in step S2, the receiver performs homodyne detection and the result is represented as |X' A +iP' A >, where:

[0017]

[0018] Where, X' A is the orthogonal position obtained by homodyne detection, P' A is the orthogonal momentum obtained by homodyne detection, i is the imaginary unit, X B is the orthogonal position of the coherent state sent by the sender, P B is the orthogonal momentum of the coherent state sent by the sender, η represents the homodyne detection efficiency, T is the transmission efficiency, δX ex Represents X' A The channel noise, δP ex Represents P' A The channel noise, δX v Represents X' A Shot noise, δP v Represents P' A Shot noise, δX el Represents X' A The electrical noise, δP el Represents P' A The electrical noise, v el is the numerical value of electrical noise.

[0019] Furthermore, in step S2, the first effective information amount is expressed as:

[0020] ΔI1=βI AB -χ AE

[0021] In the formula, ΔI1 is the first effective information amount, β is the negotiation efficiency, I AB is the Shannon mutual information between the receiver and the sender, χ AE is the Hoogland bound of the mutual information between the receiver and a possible eavesdropper, and the security threshold is greater than zero.

[0022] Furthermore, in step S3, the unitary operation D(α1) is expressed as:

[0023]

[0024] wherein, α1 is an intermediate parameter without actual meaning, is the change of quantum state mean value by the unitary operation D(α1), i is an imaginary unit, X A is the quadrature position of the coherent state received by the receiver, P A is the quadrature momentum of the coherent state received by the receiver, X u represents the first Gaussian variable of X A represents the first Gaussian variable of P u represents the first Gaussian variable of P A represents the first Gaussian variable of X u , P u satisfy Gaussian distribution wherein, α1 is an intermediate parameter without actual meaning, V is variance, χ line is the detection additional noise, χ line =1 / T+∈-1, T is transmission efficiency, ∈ is over noise in the transmission process;

[0025] The unitary operation D(α2) is represented as:

[0026]

[0027]

[0028] wherein, α2 is an intermediate parameter without actual meaning, is the change of quantum state mean value by the unitary operation D(α2), X v represents the second Gaussian variable of X A represents the second Gaussian variable of P v represents the second Gaussian variable of P A represents the second Gaussian variable of X

[0029] Further, in step S4, the second effective information quantity is represented as:

[0030] ΔI2=βI AB -χ BE

[0031] wherein, ΔI2 is the second effective information quantity, β is negotiation efficiency, I AB is the Shannon mutual information between the receiver and the sender, χ BE is the Holevo bound of mutual information between the sender and the possible eavesdropper, and the security threshold is greater than zero.

[0032] Further, in step S5, the threshold is represented as:

[0033]

[0034] wherein, is a threshold value, is the change of quantum state average value caused by unitary operation D(alpha1), is the change of quantum state average value caused by unitary operation D(alpha2).

[0035] Further, in step S6, the quantum error rate is calculated as:

[0036]

[0037] wherein, P 0err is the quantum error rate of secret information 0, P 1err is the quantum error rate of secret information 1, is a threshold value, is the change of quantum state average value caused by unitary operation D(alpha1), is the change of quantum state average value caused by unitary operation D(alpha2). u is an intermediate parameter without actual meaning, and x is an integral variable.

[0038] The present application has the following beneficial effects:

[0039] The present application uses unitary operation to express secret information, and includes two stages of security detection and information transmission. In the security detection stage, Bob and Alice randomly select partial coherent states to calculate effective information quantity, and the security of the channel is judged by comparing the effective information quantity and a security threshold value, which can avoid eavesdropping by the eavesdropper EVE and increase the security of communication. In the information transmission stage, Alice encodes secret messages through two different unitary operations on coherent states, and then sends them back to Bob. The use of unitary operation can maintain the normalization and coherence of quantum states, and ensure the integrity of information.

[0040] The present application uses continuous variable quantum states for direct communication, which continues the advantage of compatibility with standard telecommunication technology, and the coherent state has good anti-noise ability in the transmission process, which is suitable for long-distance communication. If a batch of quantum states need to be shared between Alice and Bob, Alice can load secret information on the quantum states and publish them in the standard telecommunication channel. This process is completely random for Eve, and has the same security as the classical encryption method of one-time-one-mint, i.e. absolute security. The present application uses continuous variable quantum states, which are easy to produce and detect, have small loss in the transmission process, high security, and can be compatible with standard telecommunication technology. BRIEF DESCRIPTION OF DRAWINGS

[0041] In order to make the technical solutions in the embodiments of the present application or the prior art clearer, the accompanying drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description only represent some embodiments of the present application, and other drawings can be obtained by those of ordinary skill in the art without any creative effort.

[0042] Figure 1 Flowchart of the quantum secure direct communication method based on one-time pad mode of the present application;

[0043] Figure 2 Function diagram about quantum error rate in embodiment 1 of the present application;

[0044] Figure 3 Function diagram about first effective information amount in embodiment 2 of the present application. DETAILED DESCRIPTION

[0045] The technical solutions in the embodiments of the present application will be described clearly and completely below with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments only represent some embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without any creative effort belong to the protection scope of the present application.

[0046] A quantum secure direct communication method based on one-time pad mode, comprising the following steps:

[0047] S1, a sender Bob prepares a set of coherent states A, and sends them to a receiver Alice through a quantum channel, each coherent state is represented as |X B +iP B >, wherein X B is the orthogonal position of the coherent state sent by Bob, P B is the orthogonal momentum of the coherent state sent by Bob, i is an imaginary unit, X B and P B are subject to Gaussian distribution V B is the modulation variance of Bob. The coherent state A is affected by quantum channel noise during transmission, and then the coherent state received by Alice is represented as |X A +iP A >, wherein:

[0048]

[0049] In the formula, X A is the orthogonal position of the coherent state received by Alice, P Athe quadrature momentum of the received coherent state of Alice, i is imaginary unit, δX ex represents the channel over noise of X A , δP ex represents the channel over noise of P A , δX v represents the channel over noise of X A , δP v represents the channel over noise of P A , ∈ is the over noise in the transmission process, T is the transmission efficiency, T = 10 -0.02L , L is the transmission distance.

[0050] S2, Alice randomly divides the received coherent state A into coherent state S and coherent state B, performs homodyne detection on each coherent state in the coherent state S, and the detection result is represented as |X' A +iP' A >, wherein:

[0051]

[0052] In the formula, X' A is the quadrature position obtained by homodyne detection, P' A is the quadrature momentum obtained by homodyne detection, η represents the homodyne detection efficiency, δX el represents the electrical noise of X' A , δP el represents the electrical noise of P' A , v el represents the specific value of the electrical noise.

[0053] After the detection is completed, Alice sends the quadrature position, quadrature momentum and homodyne detection result of the coherent state S to Bob, and Bob performs security detection according to the first effective information amount, and the first effective information amount is represented as:

[0054] ΔI1= βI AB -χ AE

[0055]

[0056] In the formula, ΔI1 is the first effective information amount, β is the negotiation efficiency, I AB is the Shannon mutual information between Alice and Bob, χ AE is the Holevo bound of mutual information between Alice and possible eavesdropper Eve, V is the variance, χ tot is the total noise of the channel input, χ tot = χ line + χ hom / T, χ homis the oscillator homomorphic noise, χ line To detect the additional noise, χ line =1 / T+∈-1, S is the von Neumann entropy, is the first quantum state, is the second quantum state.

[0057] Considering the Gaussian state G(x) in the first effective information derivation, it can be further simplified as:

[0058]

[0059] where G(x) = (x+1)log2(x+1)-xlog2x, λ i is the symplectic eigenvalue.

[0060] First quantum state The covariance matrix of for:

[0061]

[0062] Among them is The identity matrix, is the Pauli matrix, diag is the matrix constructor;

[0063] satisfy:

[0064]

[0065] Where λ 1,2 is the covariance matrix The corresponding symplectic eigenvalues, A and B are intermediate parameters with no practical significance, where:

[0066] A=V 2 +T 2 (V+χ line ) 2 -2T(V 2 -1)

[0067] B=T 2 (χ line +1) 2

[0068] Similarly, the second quantum state The covariance matrix of λ 3,4,5 is the covariance matrix The corresponding symplectic eigenvalues ​​satisfy:

[0069]

[0070] C is an intermediate parameter without practical significance, wherein:

[0071]

[0072] The security threshold is set to be greater than zero, if the first effective information amount is greater than the security threshold, the next step is performed, if the first effective information amount is less than the security threshold, it is indicated that there is an attack, and the communication is abandoned.

[0073] S3, Alice encodes the coherent state B according to the secret information, if the secret message sent is 0, a unitary operation D (α1) is selected for encoding, and is:

[0074]

[0075] In the formula, α1 is an intermediate parameter without practical significance, is the change of the mean value of the quantum state by the unitary operation D (α1), X u represents the first Gaussian variable of X A , P u represents the first Gaussian variable of P A , which satisfies the Gaussian distribution σ u is an intermediate parameter without practical significance, T is the transmission efficiency;

[0076] If the secret message sent is 1, a unitary operation D (α2) is selected for encoding, and is:

[0077]

[0078] In the formula, α2 is an intermediate parameter without practical significance, is the change of the mean value of the quantum state by the unitary operation D (α2), X v represents the second Gaussian variable of X A , P v represents the second Gaussian variable of P A .

[0079] Alice sends the encoded coherent state B to Bob through a standard telecommunication channel.

[0080] S4, Bob randomly selects a coherent state from the received coherent state B to perform homodyne detection, after the detection is completed, Bob sends the orthogonal position, orthogonal momentum and homodyne detection result of the coherent state to Alice, and Alice performs security detection according to the second effective information amount, and the second effective information amount is represented as:

[0081] ΔI2=βI AB -χ BE

[0082] Wherein, ΔI2 is the second effective information amount, β is the negotiation efficiency, I AB is the Shannon mutual information between Alice and Bob, χ BE is the Holevo bound of the mutual information between Bob and the possible eavesdropper Eve;

[0083] A security threshold is set, the security threshold is greater than zero, if the second effective information amount is greater than the security threshold, the next step is carried out, and if the second effective information amount is less than the security threshold, the communication is abandoned.

[0084] S5, Bob performs homodyne detection on the remaining coherent state B and calculates a threshold, which is expressed as:

[0085]

[0086] Wherein, is the threshold;

[0087] If the homodyne detection result is less than the threshold, Bob considers that Alice is performing the unitary operation D (α1), and demodulates to obtain the secret information 0, and if the homodyne detection result is greater than the threshold, Bob considers that Alice is performing the unitary operation D (α2), and demodulates to obtain the secret information 1.

[0088] S6, after demodulation, Bob calculates the quantum error rate of the secret information 0 and 1, and judges whether the quantum channel is safe according to the quantum error rate, and the quantum error rate is:

[0089]

[0090] Wherein, P 0err is the quantum error rate of the secret information 0, P 1err is the quantum error rate of the secret information 1, σ u is an intermediate parameter without actual meaning, and x is an integral variable.

[0091] As shown in Figure 1 , it is a flowchart of the quantum secure direct communication method based on one-time pad mode.

[0092] Embodiment 1

[0093] A quantum communication is carried out by using the quantum secure direct communication method based on one-time pad mode provided by the application, and the setting is The setting is 1, 4, 7, respectively, and the quantum error rate is detected, and the result is shown in Figure 2 , it can be seen that the parameter The value of can reduce the quantum bit error rate, that is, setting two unitary operations D(α1) and D(α2) with a large difference can obtain better performance. In addition, choosing a smaller modulation variance over a shorter transmission distance can further reduce the quantum bit error rate.

[0094] Example 2

[0095] The quantum communication is performed by using a quantum secure direct communication method based on a one-time pad mode provided by the present invention, and setting ∈ = 0.05, β = 0.95, v el =0.01, η=0.6, detection modulation variance V B The influence of transmission distance on the first effective information volume, such as Figure 3 As shown, it can be seen that the first effective information amount slowly decreases as the modulation variance increases in the transmission distance. In the figure, 80% ΔImax(U) and 80% ΔImax(L) represent the upper and lower dividing lines of 80% of the optimal value of the first effective information amount. It can be seen that the optimal value of the first effective information amount can be obtained by selecting the corresponding modulation variance according to the transmission distance.

[0096] Each embodiment in this specification is described in a related manner. Similar parts between the various embodiments can be referred to in conjunction with each other. Each embodiment focuses on the differences between the other embodiments. In particular, the system embodiment is generally similar to the method embodiment, so the description is relatively simple. For related parts, refer to the description of the method embodiment.

[0097] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention are included in the scope of protection of the present invention.

Claims

1. A quantum secure direct communication method based on a one-time pad mode, characterized in that, The method comprises the following steps: S1, the sender prepares a set of coherent states A and sends them to the receiver through a quantum channel; S2, the receiver randomly divides the received coherent states A into coherent states S and coherent states B, performs homodyne detection on each coherent state in the coherent states S, and sends the quadrature position, quadrature momentum and homodyne detection result of the coherent states S to the sender, the sender performs security detection according to the first effective information quantity, if the first effective information quantity is greater than the security threshold, the next step is performed, if the first effective information quantity is less than the security threshold, the communication is abandoned; S3, the receiver encodes the coherent states B according to the secret information, if the secret information sent is 0, the unitary operation D(α1) is used for encoding, if the secret information sent is 1, the unitary operation D(α2) is selected for encoding, and the encoded coherent states B are sent to the sender; S4, the sender randomly selects one coherent state from the received coherent states B to perform homodyne detection, and sends the quadrature position, quadrature momentum and homodyne detection result of the coherent state to the receiver, the receiver performs security detection according to the second effective information quantity, if the second effective information quantity is greater than the security threshold, the next step is performed, if the second effective information quantity is less than the security threshold, the communication is abandoned; S5, the sender performs homodyne detection on the remaining coherent states B and calculates a threshold, if the homodyne detection result is less than the threshold, the sender considers that the receiver is performing unitary operation D(α1), and demodulates to obtain secret information 0, if the homodyne detection result is greater than the threshold, the sender considers that the receiver is performing unitary operation D(α2), and demodulates to obtain secret information 1; S6, after demodulation, the sender calculates the quantum error rate of secret information 0 and 1, and judges whether the quantum channel is safe according to the quantum error rate.

2. The quantum secure direct communication method based on one-time pad mode according to claim 1, characterized in that, In step S1, the coherent state A received by the receiver is represented as |X A +iP A >, wherein: where X A is the quadrature position of the coherent state received by the receiver, P A is the quadrature momentum of the coherent state received by the receiver, X B is the quadrature position of the coherent state sent by the sender, P B is the quadrature momentum of the coherent state sent by the sender, i is the imaginary unit, δX ex represents the channel excess noise of X A , δP ex represents the channel excess noise of P A , δX v represents the shot noise of X A , δP v represents the shot noise of P A , ∈ is the excess noise in the transmission process, T is the transmission efficiency, T = 10 -0.02L , L is the transmission distance, V B is the modulation variance of the sender.

3. The quantum secure direct communication method based on one-time pad mode according to claim 1, characterized in that, In step S2, the receiver performs homodyne detection and the result is represented as |X A + iP A >, where: where X' is the quadrature position of the homodyne detection result, P' is the quadrature momentum of the homodyne detection result, i is the imaginary unit, X is the quadrature position of the coherent state sent by the sender, P is the quadrature momentum of the coherent state sent by the sender, η represents the homodyne detection efficiency, T is the transmission efficiency, δX represents the channel over noise of X', δP represents the channel over noise of P', δX represents the shot noise of X', δP represents the shot noise of P', δX represents the electrical noise of X', δP represents the electrical noise of P', v is the numerical size of the electrical noise. A A B B ex A ex A v A v A el A el A el where X' is the quadrature position of the homodyne detection result, P' is the quadrature momentum of the homodyne detection result, i is the imaginary unit, X is the quadrature position of the coherent state sent by the sender, P is the quadrature momentum of the coherent state sent by the sender, η represents the homodyne detection efficiency, T is the transmission efficiency, δX represents the channel over noise of X', δP represents the channel over noise of P', δX represents the shot noise of X', δP represents the shot noise of P', δX represents the electrical noise of X', δP represents the electrical noise of P', v is the numerical size of the electrical noise.​​​​​​​​​​​​​​​​ 4. The quantum secure direct communication method based on one-time pad mode according to claim 1, characterized in that, In step S2, the first effective information quantity is represented as: ΔI1 = βI AB -χ AE where ΔI1 is the first effective information amount, β is the negotiation efficiency, I AB is the Shannon mutual information between the receiver and the sender, χ AE is the Hoggale bound of the mutual information between the receiver and the potential eavesdropper The security threshold is greater than zero.

5. The quantum secure direct communication method based on one-time pad mode according to claim 1, characterized in that, In step S3, the unitary operation D(α1) is represented as: In the formula, α1 is an intermediate parameter without practical significance, Q is the change of the unitary operation D(α1) on the quantum state average, i is an imaginary unit, X A is the orthogonal position of the coherent state received by the receiver, P A is the orthogonal momentum of the coherent state received by the receiver, X u represents the first Gaussian variable of X A , P u represents the first Gaussian variable of P A , X u , P u satisfy Gaussian distribution is an intermediate parameter without practical significance, V is a variance, χ line is a detection additional noise, χ line =1 / T+∈-1, T is a transmission efficiency, and ∈ is an over noise in the transmission process. The unitary operation D(α2) is represented as: In the formula, α2 is an intermediate parameter without actual meaning, is the change of the quantum state average value under the unitary operation D(α2), X v represents the second Gaussian variable of X A , P v represents the second Gaussian variable of P A .

6. The quantum secure direct communication method based on one-time pad mode according to claim 1, characterized in that, In step S4, the second effective information quantity is represented as: ΔI2 = βI AB -χ BE where ΔI2 is the second effective information amount, β is the negotiation efficiency, I AB is the Shannon mutual information between the receiver and the sender, χ BE is the Hoggale bound of the mutual information between the sender and the possible eavesdropper. The security threshold is greater than zero.

7. The quantum secure direct communication method based on one-time pad mode according to claim 1, characterized in that, In step S5, the threshold is represented as: wherein is a threshold value, is the change in the quantum state mean value by the unitary operation D(a2), is the change in the quantum state mean value by the unitary operation D(a2).

8. The quantum secure direct communication method based on one-time pad mode according to claim 1, characterized in that, In step S6, the quantum error rate is calculated as: where P 0err is the quantum error rate of secret information 0, P 1err is the quantum error rate of secret information 1, is a threshold value, is the change of quantum state average value caused by unitary operation D(α1), is the change of quantum state average value caused by unitary operation D(α2), σ u is an intermediate parameter without actual meaning, and x is an integral variable.

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