A semi-quantum secure direct communication method that is resistant to collective phase shift noise and collective rotation noise

Abstract

The present invention discloses a semi-quantum secure direct communication method that is resistant to collective phase shift noise and collective rotation noise. According to the characteristics of the six-qubit decoherence-free state, a new coding mapping rule is proposed to help a classical sender to securely transmit secret messages to a quantum receiver in a quantum channel containing collective noise without interference. Secondly, in the secret message transmission stage, the message authentication technology in classical cryptography is introduced to implement secondary encryption of the secret message to ensure the authenticity and integrity of the secret message. Finally, the secret message is recovered by six single-particle measurement technologies, which is highly feasible.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum secure communication, and in particular to a semi-quantum secure direct communication method capable of resisting collective phase shift noise and collective rotation noise. Background Art

[0002] In recent years, in order to reduce or eliminate the impact of collective noise on quantum communication, the concept of decoherence-free subspace has been proposed. Decoherence-free subspace refers to a subspace in Hilbert space that does not experience coherence. Each state in the subspace is composed of several quantum bits that are subject to the same noise interference, and the system composed of them can compensate for the impact of noise so that the quantum state of the system remains unchanged in a noisy environment. This advantage can be used to encode information and complete quantum communication under collective noise. At present, decoherence theory has been widely used in the field of quantum secure direct communication.

[0003] In 2007, Ge and Liu proposed a method for quantum secure direct communication based on decoherence-free subspace, which is highly robust on collective phase noise channels. In 2010, Qin proposed a method for quantum secure direct communication based on decoherence-free subspace, which can resist collective rotation noise. In 2011, Yang proposed two fault-tolerant two-step quantum secure direct communication methods based on the theory of decoherence-free subspace, each of which can resist different types of collective noise and has strong scalability. In 2012, Yang improved the method proposed by Ge and Liu, which is a shortcoming that attackers can deliberately modify messages without being discovered, and perfected quantum secure direct communication on collective phase noise channels. In 2014, Yang et al. proposed two fault-tolerant controlled quantum secure direct communication methods based on the theory of controlled quantum secure direct communication and decoherence-free subspace, which are robust to both collective phase noise and collective rotation noise. In 2015, Li, Song and others proposed a method of quantum secure communication using the decoherence-free state, which can not only resist collective decoherence noise but also reduce the loss of photons.

[0004] It can be seen from the above academic research and application scenarios that, as of now, in the field of semi-quantum secure direct communication, that is, there are several classical parties in the communication, and the rest are quantum parties, a method that can simultaneously resist collective phase shift noise and collective rotation noise has not yet been proposed. Summary of the invention

[0005] The purpose of the present invention is to make up for the shortcomings of the existing methods, and propose a method of semi-quantum secure direct communication that is robust to both collective noises based on the quantum non-decoherent state, so as to alleviate or solve the channel collective noise problem faced in common semi-quantum communication. In addition, the present invention mentions a new coding rule, which can be used by the classical sender to transmit secret messages to the quantum receiver securely in a quantum channel containing collective noise without interference. At the same time, in the message transmission stage, the authenticity and integrity of the secret message are guaranteed by combining the message authentication technology in classical cryptography.

[0006] The present invention provides a semi-quantum secure direct communication method that resists collective phase shift noise and collective rotation noise, and the detailed implementation method and steps involved are as follows, including:

[0007] S101, Alice prepares 2N six-qubit decoherence-free states to form a sequence S = {s1, s2, …, s i ,…,s 2N},in i=1,2,…,2N, q is a single-particle state, N is an integer, and each six-qubit decoherence-free state comes from the quantum carrier |ρ2>; Alice takes out N six-qubit decoherence-free states as bait photons, divides them into two sequences S1 and S2, and sends S1 to Bob, retaining S2 and the remaining N six-qubit decoherence-free states;

[0008] S102, after receiving the S1 sequence, Bob randomly performs measurement or reflection operations on each quantum state in it to feed back the state to Alice;

[0009] S103, after Alice confirms that she has received the status sent back by Bob, Bob publishes the corresponding operations and measurement results, and Alice conducts the first eavesdropping detection: Based on the detection results, Alice obtains the error rate. If the error rate exceeds the predetermined security threshold, the communication will be terminated; otherwise, it means that the quantum channel is secure, and proceed to S104;

[0010] S104, after passing the eavesdropping detection, Alice performs a quantum position permutation operation on the remaining N six-qubit decoherence-free states |ρ2> according to the coding rules to form sequences S3 and S4. Alice shuffles the order of S2, S3, and S4 to obtain sequence S5, and sends S5 to Bob;

[0011] S105, after Bob receives sequence S5, Alice announces the original sequence corresponding to S2. At this time, Bob and Alice repeat the operations of steps S102 and S103 to conduct a second eavesdropping check to ensure that the quantum state is not disturbed. After passing the eavesdropping check, Alice announces the initial sequence of S3 and S4, and Bob uses the message authentication algorithm MAC, that is, a one-way hash function H controlled by the key K. K (·) to encrypt the secret message sequence m; then, Bob calculates MAC = H K (m) and M = m||MAC, where || represents the "connection" operation; in order to eliminate the influence of channel noise, Bob randomly places the corresponding M according to the position of the state |ρ3> and |ρ4> i Encoded into sequences S3 and S4, where M i represents the i-th value of M, that is, if M i is 0, then the code is |ρ3>; if M i If it is 1, it is encoded as |ρ4>; after encoding, Bob forms it into sequence S6 and sends it to Alice;

[0012] S106, after receiving S6, Alice performs basis set measurement on each of the six quantum bits in the decoherence-free state. The purpose of performing this operation is to achieve a similar effect to the reflection operation in the first and second eavesdropping inspections, and to distinguish the received quantum states. Alice compares the measurement results of |ρ3> and |ρ4> in S6 with the initial measurement results, and infers M'=m'||MAC' based on the comparison results, encoding rules and key K. Alice compares MAC=H K (m') and MAC' = H K (m)' are equal. If they are equal, the authentication is valid, indicating that the message has not been tampered with and the communication is successful; otherwise, the authentication is invalid, indicating that the message has been tampered with and the communication has failed.

[0013] In one implementation, step S102 specifically includes:

[0014] If the measurement operation is selected, Bob performs a Z-basis measurement on each qubit in the six-qubit decoherence-free state, generates corresponding states based on the measurement results, and sends these states back to Alice;

[0015] If the reflection operation is chosen, Bob will reflect the six-qubit non-decoherent state back to Alice without interference.

[0016] In one implementation, step S103 includes:

[0017] If it is a measurement operation, Alice also performs a Z-basis measurement on each qubit of the received particle to see if the result is the same as the one published by Bob;

[0018] If it is a reflection operation, then based on the initial six-qubit non-decoherence state, Alice uses the corresponding basis set to measure the received state and observe whether it is the same as the initial state.

[0019] In one implementation, the specific operations of step S104 include:

[0020] Alice chooses The quantum carrier |ρ2> state performs the 1st, 3rd and 2nd, 4th quantum position exchange to obtain the quantum carrier |ρ3>, forming a sequence S3;

[0021] Alice The quantum carrier |ρ2> state performs the 1st, 5th and 2nd, 6th quantum position permutations to obtain the quantum carrier |ρ4>, forming the sequence S4; Alice scrambles the order of S2, S3 and S4 to obtain the sequence S5, and sends S5 to Bob.

[0022] In one implementation, the specific expression of the quantum carrier includes:

[0023]

[0024] |ρ3>=P 24 P 13 |ρ2>

[0025] |ρ4>=P 26 P 15 |ρ2>

[0026] in,

[0027]

[0028] P 13 Indicates that the first and third qubits are replaced, P 24 Indicates that the second and fourth qubits are replaced, P 15 Indicates that the 1st and 5th quantum bits are replaced, P 26 It means that the 2nd and 6th quantum bits are replaced.

[0029] In one implementation, if M i is 0, then encode it as |ρ3>; if M i is 1, then the encoding is |ρ4>.

[0030] The semi-quantum secure direct communication method for resisting collective phase shift noise and collective rotation noise provided by the embodiment of the present invention has the following beneficial effects:

[0031] Compared with the existing methods, the present invention utilizes the quantum non-cloning theorem and the Heisenberg uncertainty principle, and based on the characteristics of the non-decoherent subspace, proposes a method in the semi-quantum field that can simultaneously resist two types of collective noise, broadens the scope of use of quantum secure communication, and also reduces the cost of technical implementation. Specifically, it has the following advantages:

[0032] 1. Based on the six-qubit decoherence-free state, the present invention proposes a method for semi-quantum secure direct communication that is robust to both collective phase shift noise and collective rotation noise, alleviating the channel collective noise problem existing in existing semi-quantum secure communications.

[0033] 2. The present invention combines the message authentication technology in classical cryptography to ensure the authenticity and integrity of information transmission and has high anti-attack capability.

[0034] 3. The preparation of the initial six-qubit decoherence-free state quantum carrier involved in the present invention can be obtained on the basis of lower-dimensional quantum decoherence-free states (2 and 4 qubits), which increases the convenience and feasibility of the implementation of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a structural schematic diagram of a semi-quantum secure direct communication method for resisting collective phase shift noise and collective rotation noise according to an embodiment of the present invention.

[0036] Figure 2 It is a coding rule mapping diagram for realizing semi-quantum secure direct communication against two kinds of collective noises in the decoherence-free state of quantum bits in embodiment six of the present invention.

[0037] Figure 3 Schematic diagram of distinguishing any two six-qubit decoherence-free states for single-particle measurements.

[0038] Figure 4 The present invention is a flow chart of a method for message authentication technology. DETAILED DESCRIPTION

[0039] The following describes the embodiments of the present invention through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention.

[0040] The illustrations provided in this embodiment are only used to illustrate the basic concept of the present invention in a schematic manner. Therefore, the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0041] 1. Preparation of quantum decoherence-free state

[0042] There are five main forms of six-qubit decoherence-free states:

[0043]

[0044] in,

[0045]

[0046] |ρ5> is calculated using the Gram-Schmidt method, where t is the number of transitions of pairs of elements that must be composed to place the elements in canonical order (i.e., 000111).

[0047] Three of the states are selected as quantum carriers, namely |ρ2>, |ρ3> and |ρ4>. According to the characteristics of the six-qubit decoherence-free state, one of the states |ρ2> is prepared first, and then the other two states |ρ3> and |ρ4> can be obtained by replacing the qubits in this state, as shown in the following transformation:

[0048] |ρ3>=P 24 P 13 |ρ2>

[0049] |ρ4>=P 26 P 15 |ρ2>

[0050] 2. Design of encoding mapping rules

[0051] (1) If the sender's secret information bit is 0, then the 1st, 3rd and 2nd, 4th qubits in |ρ2> are permuted to obtain the state |ρ3>;

[0052] (2) If the sender’s secret information bit is 1, then the 1st, 5th and 2nd, 6th qubits in |ρ2> are permuted to obtain the state |ρ4>.

[0053] Among them, a certain proportion of the initial state |ρ2> is used as bait photons for eavesdropping detection. After the encoding is completed, the receiver performs a fixed single-particle measurement on the coded state sent by the sender, observes the measurement results, distinguishes the received states |ρ3> and |ρ4>, and thus recovers the secret message based on the corresponding relationship.

[0054] 3. Message Authentication Technology

[0055] Combined with the hash encryption algorithm in classical cryptography, it is implemented. Assuming that the two communicating parties share a key K, the sender A wants to send a message m to the receiver B. The detailed execution steps are described as follows:

[0056] A uses the MAC algorithm to encode the message, that is, calculate MAC = H K (m), where H K (·) is a public function controlled by the key K (such as a hash function);

[0057] A sends |ρ3> to B through an open channel (where || represents a "connect" operation);

[0058] After receiving it, B performs the same calculation as A and obtains a new MAC;

[0059] B observes whether the received MAC is equal to the obtained new MAC. If they are equal, the authentication is valid, and vice versa.

[0060] 4. Single particle measurement technology

[0061] The six-qubit decoherence-free state can be used as a quantum carrier for communication because it can fully protect two arbitrary logical quantum states from the influence of collective noise, and can distinguish any two of them through a fixed six single-particle basis measurements. It is suitable for semi-quantum environments. The specific measurement and distinction methods are shown in Table 1 below:

[0062] Table 1

[0063]

[0064] The technical solution of the present invention is to design a feasible coding mapping rule based on the characteristics of the six-qubit decoherence-free state, including using the six-qubit decoherence-free state and encrypting the classical secret bits 0 and 1; and combining the classical message authentication code technology to realize secondary encryption of the secret message; finally, by executing six single-particle ZZXXZZ basis set measurement technology, combined with message authentication, the encrypted message is recovered. The encryption, authentication and measurement technologies involved in the method can be realized under existing conditions.

[0065] Figure 1 The figure shows the overall method route diagram of using quantum decoherence-free state to achieve semi-quantum secure direct communication against two collective noises. Alice and Bob share the key K in advance. The implementation principle can be roughly divided into the following steps:

[0066] S101, Alice prepares 2N six-qubit decoherence-free states to form a sequence S = {s1, s2, …, s i,…,s 2N},in i=1,2,…,2N, q is a single-particle state, N is an integer, and each six-qubit non-decoherence state comes from the ground state |ρ2>. Then Alice takes out N six-qubit non-decoherence states as bait photons, divides them into two sequences S1 and S2, and sends S1 to Bob, retaining S2 and the remaining N six-qubit non-decoherence states.

[0067] The present invention uses three types of six-qubit decoherence-free states as carriers, namely |ρ2>, |ρ3> and |ρ4>, as follows:

[0068]

[0069]

[0070] in,

[0071]

[0072] According to their characteristics, we only need to prepare one of the states |ρ2>, and then by replacing the qubits in this state, we can obtain the other two states |ρ3> and |ρ4>, as shown in the following transformation:

[0073] |ρ3>=P 24 P 13 |ρ2>

[0074] |ρ4>=P 26 P 15 |ρ2>

[0075] If the sender's secret information bit is 0, the 1st, 3rd and 2nd, 4th quantum bits in |ρ2> are replaced to obtain the state |ρ3>; if the sender's secret information bit is 1, the 1st, 5th and 2nd, 6th quantum bits in |ρ2> are replaced to obtain the state |ρ4>. The corresponding encoding mapping relationship is as follows: Figure 2 As shown in Figure 2, a certain proportion of the initial state |ρ2> is used as decoy photons for eavesdropping detection. After the encoding is completed, the receiver performs a fixed single-particle measurement on these encoded states sent by the sender, as shown in Figure 2. Figure 3 As shown, the measurement results are observed to distinguish the received states |ρ3> and |ρ4>, thereby recovering the secret message based on the corresponding relationship.

[0076] S102, after receiving the S1 sequence, Bob randomly performs measurement or reflection operations on each quantum state therein.

[0077] If the measurement operation is selected, Bob performs a Z-basis measurement on each qubit in the six-qubit decoherence-free state, generates corresponding states based on the measurement results, and sends these states back to Alice;

[0078] If the reflection operation is chosen, Bob will reflect the six-qubit non-decoherent state back to Alice without interference.

[0079] S103, when Alice confirms receipt of the status sent back by Bob, Bob publishes the corresponding operations and measurement results, and Alice conducts the first eavesdropping detection:

[0080] If it is a measurement operation, Alice also performs a Z-basis measurement on each qubit of the received particle to see if the result is the same as the one published by Bob;

[0081] If it is a reflection operation, then based on the initial six-qubit non-decoherence state, Alice uses the corresponding basis set to measure the received state and observe whether it is the same as the initial state.

[0082] After the detection is completed, Alice will obtain an error rate. If the error rate exceeds the predetermined security threshold, the communication will be terminated; otherwise, it means that the quantum channel is secure and proceed to the next step.

[0083] S104, after passing the eavesdropping detection, Alice performs a quantum position swap operation on the remaining N six-qubit decoherence-free states |ρ2> according to the coding rules: Here, for the convenience of calculation, we choose to perform a quantum position swap operation on the remaining N six-qubit decoherence-free states |ρ2>. The |ρ2> state performs the 1st, 3rd and 2nd, 4th quantum position exchange to obtain |ρ3>, forming sequence S3; The |ρ2> states perform the 1st, 5th and 2nd, 6th quantum position swaps to obtain |ρ4>, forming the sequence S4. Then, Alice shuffles the order of S2, S3 and S4 to obtain the sequence S5, and sends S5 to Bob.

[0084] S105, after Bob receives sequence S5, Alice announces the original sequence corresponding to S2. At this time, Bob and Alice repeat the operations of steps S102 and 103 to conduct a second eavesdropping check to ensure that the quantum state is not disturbed. After passing the eavesdropping check, Alice announces the initial sequence of S3 and S4. At this time, Bob uses the message authentication algorithm MAC (corresponding to Figure 4 ), that is, using a one-way hash function H controlled by the key K K (·)(i.e. H():{0,1} k →{0,1} d , where k represents the length of the input data and d represents the length of the output hash value) to encrypt the secret message sequence m; then, Bob calculates MAC = HK (m) and M = m||MAC (where || represents the "connection" operation); in order to eliminate the influence of channel noise, Bob randomly replaces the corresponding M according to the position of the state |ρ3> and |ρ4> i Encoded into sequences S3 and S4, where M i represents the i-th value of M, that is, if M i is 0, then the code is |ρ3>; if M i If it is 1, it is encoded as |ρ4>. After encoding, Bob forms it into sequence S6 and sends it to Alice.

[0085] S106, after Alice receives S6, she performs a ZZXXZZ basis set measurement on each of the six quantum bits in the decoherence-free state. The purpose of performing this operation is to achieve a similar effect to the reflection operation in the first and second eavesdropping inspections, and to distinguish the received quantum states. Afterwards, Alice compares the measurement results of |ρ3> and |ρ4> in S6 with the initial measurement results, and infers M'=m'||MAC' based on the comparison results, encoding rules and key K. Next, Alice compares MAC=H K (m') and MAC' = H K (m)' are equal. If they are equal, the authentication is valid, indicating that the message has not been tampered with and the communication is successful; otherwise, the authentication is invalid, indicating that the message has been tampered with and the communication has failed.

[0086] The above embodiments are merely illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Anyone familiar with the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by a person of ordinary skill in the art without departing from the spirit and technical concept disclosed by the present invention shall still be covered by the claims of the present invention.

Claims

1. A semi-quantum secure direct communication method that resists collective phase shift noise and collective rotation noise, characterized in that: include: S101, Alice prepares 2N six-qubit decoherence-free states to form a sequence S = {s1, s2, …, s i ,…,s 2N },in i=1,2,…,2N, q is a single-particle state, N is an integer, and each six-qubit decoherence-free state comes from the quantum carrier |ρ2>; Alice takes out N six-qubit decoherence-free states as bait photons, divides them into two sequences S1 and S2, and sends S1 to Bob, retaining S2 and the remaining N six-qubit decoherence-free states; S102, after receiving the S1 sequence, Bob randomly performs measurement or reflection operations on each quantum state in it to feed back the state to Alice; S103, after Alice confirms that she has received the status sent back by Bob, Bob publishes the corresponding operations and measurement results, and Alice conducts the first eavesdropping detection: Based on the detection results, Alice obtains the error rate. If the error rate exceeds the predetermined security threshold, the communication will be terminated; otherwise, it means that the quantum channel is secure, and proceed to S104; S104, after passing the eavesdropping detection, Alice performs a quantum position permutation operation on the remaining N six-qubit decoherence-free states |ρ2> according to the coding rules to form sequences S3 and S4. Alice shuffles the order of S2, S3, and S4 to obtain sequence S5, and sends S5 to Bob; S105, after Bob receives sequence S5, Alice announces the original sequence corresponding to S2. At this time, Bob and Alice repeat the operations of steps S102 and S103 to conduct a second eavesdropping check to ensure that the quantum state is not disturbed. After passing the eavesdropping check, Alice announces the initial sequence of S3 and S4. Bob uses the message authentication algorithm MAC and the one-way hash function H controlled by the key K. K (·) to encrypt the secret message sequence m; then, Bob calculates MAC = H K (m) and M = m||MAC, where || represents the "connection" operation; in order to eliminate the influence of channel noise, Bob randomly places the corresponding M according to the position of the state |ρ3> and |ρ4> i Encoded into sequences S3 and S4, where M i represents the i-th value of M, that is, if M i is 0, then the code is |ρ3>; if M i If it is 1, it is encoded as |ρ4>; after encoding, Bob forms it into sequence S6 and sends it to Alice; S106, after receiving S6, Alice performs basis set measurement on each of the six qubits in the decoherence-free state. Alice compares the measurement results of |ρ3> and |ρ4> in S6 with the initial measurement results, and infers M'=m'||MAC' based on the comparison results, encoding rules and key K. Alice compares MAC=H K (m') and MAC' = H K (m) 'Are they equal? ​​If they are equal, the authentication is valid, indicating that the message has not been tampered with and the communication is successful; Otherwise, the authentication is invalid, indicating that the message has been tampered with and the communication has failed.

2. A semi-quantum secure direct communication method for resisting collective phase shift noise and collective rotation noise according to claim 1, characterized in that: The step S102 specifically includes: If the measurement operation is selected, Bob performs a Z-basis measurement on each qubit in the six-qubit decoherence-free state, generates corresponding states based on the measurement results, and sends these states back to Alice; If the reflection operation is chosen, Bob will reflect the six-qubit non-decoherent state back to Alice without interference.

3. The semi-quantum secure direct communication method for resisting collective phase shift noise and collective rotation noise according to claim 1, characterized in that: The step S103 includes: If it is a measurement operation, Alice also performs a Z-basis measurement on each qubit of the received particle to see if the result is the same as the one published by Bob; If it is a reflection operation, then based on the initial six-qubit decoherence-free state, Alice uses the corresponding basis set to measure the received state and observe whether it is the same as the initial state.

4. The semi-quantum secure direct communication method for resisting collective phase shift noise and collective rotation noise according to claim 1, characterized in that: The specific operations of step S104 include: Alice chooses The quantum carrier |ρ2> state performs the 1st, 3rd and 2nd, 4th quantum position exchange to obtain the quantum carrier |ρ3>, forming a sequence S3; Alice The quantum carrier |ρ2> state performs the 1st, 5th and 2nd, 6th quantum position permutations to obtain the quantum carrier |ρ4>, forming the sequence S4; Alice scrambles the order of S2, S3 and S4 to obtain the sequence S5, and sends S5 to Bob.

5. The semi-quantum secure direct communication method for resisting collective phase shift noise and collective rotation noise according to claim 4, characterized in that: The specific expressions of quantum carriers include: |ρ3>=P 24 P 13 |ρ2> |ρ4>=P 26 P 15 |p2> in, P 13 Indicates that the first and third qubits are replaced, P 24 Indicates that the second and fourth qubits are replaced, P 15 Indicates that the 1st and 5th quantum bits are replaced, P 26 It means that the 2nd and 6th quantum bits are replaced.

6. The semi-quantum secure direct communication method for resisting collective phase shift noise and collective rotation noise according to claim 5, characterized in that: If M i is 0, it is encoded as |ρ3>; if M i is 1, it is encoded as |ρ4>.

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