Implementation method and system of a fully reference frame independent quantum key distribution protocol

Abstract

This invention discloses a method and system for implementing a completely reference-frame-independent quantum key distribution protocol, belonging to the field of quantum information technology. Alice and Bob, the communicating parties, randomly select mutually unbiased basis vectors to prepare quantum states and send them to a third party, Charlie. Charlie performs Bell state projection measurements and announces the success. Both parties publish the basis vector information, divide the dataset, and calculate the gain and bit error rate. A 3×3 correlation tensor matrix is ​​constructed and singular value decomposition is performed to obtain three reference-frame-independent singular values. The secure key rate is calculated based on the bit error rate. Finally, key negotiation and security enhancement are performed to extract the secure key. This invention does not require basis vector alignment, completely eliminating the dependence on reference frame calibration. It can still stably generate keys even with basis vector drift, and the amount of information required by eavesdroppers is lower, significantly improving the practicality and security of the quantum key distribution system.

Description

Technical Field

[0001] This invention relates to the field of quantum information technology, and specifically to a method and system for implementing a completely reference frame-independent quantum key distribution protocol. Background Technology

[0002] Based on the fundamental principles of quantum mechanics, quantum key distribution (QKD) allows information-theoretically secure keys to be distributed between Alice and Bob. In most QKD systems, Alice and Bob need to establish a common frame of reference to achieve correct encoding and decoding. On a Bloch sphere, the frame of reference can be determined by polarization angles. Azimuth and the relative phase between the two calculated ground state vectors To characterize this, Alice and Bob would typically need to perform real-time calibration to share a reference frame. However, real-time calibration reduces the key rate of a QKD system and increases its implementation complexity. Fortunately, reference-frame-independent QKD protocols can still generate secure keys even when the reference frame is unknown and slowly changing. Reference-frame-independent QKD protocols include reference-frame-independent QKD (RFI-QKD) and reference-frame-measurement-device-independent QKD (RFI-MDI-QKD). The RFI-MDI-QKD protocol is immune to slow drift in the reference frames of both communicating parties and can also prevent all attacks targeting the measurement device by eavesdroppers. However, this type of protocol relies on a stringent assumption: the coding basis vectors of Alice and Bob... The requirement is that it is well-defined and stable, i.e. Based on this alignment The information about Eve, the eavesdropper, is independent of the unknown and slowly drifting test base. and .

[0003] However, in some practical applications, achieving stable and accurate alignment of the code basis vectors is extremely challenging. If the code basis vectors are not aligned, the security assumptions of RFI-MDI-QKD cannot be satisfied, and eavesdroppers can steal more information during the key generation process. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for implementing a completely reference frame-independent quantum key distribution protocol, in order to solve the problems in existing reference frame measurement devices' dual-independent quantum key distribution protocols, such as the need for precise alignment of the code basis vectors to ensure security and the difficulty of real-time reference frame calibration in practical applications.

[0005] To achieve the above objectives, the technical solution provided by this invention is: a method for implementing a completely reference-frame-independent quantum key distribution protocol, comprising the following steps: S1: Alice and Bob, the communicating parties, randomly select their local unbiased basis vectors and corresponding coded bits, prepare the corresponding quantum states, and send the prepared quantum states to Charlie, the third party, through a quantum channel; the unbiased basis vectors include coded basis vectors. and test basis vectors and ; S2: Charlie, a third party, performs Bell projection measurement on the received quantum state and announces the measurement result to Alice and Bob via a public channel whether the measurement was successful; if the measurement is unsuccessful, the corresponding quantum state is discarded. S3: Alice and Bob, the communicating parties, announce the successfully measured quantum state to Charlie, a third party, and publish the basis vector information used in preparing their respective quantum states through a public channel. Based on the basis vector information, they combine their respective bits according to the basis vectors. Divided into different datasets Alice and Bob, the two communicating parties, randomly sample a portion of bits from each dataset and calculate the gain and bit error rate of the qubits under that basis vector combination. S4: Construct a 3×3 correlation tensor matrix that represents the shared quantum state between the communicating parties. Perform singular value decomposition on this correlation tensor matrix to obtain three singular values ​​that are independent of the choice of reference frame. Combine the singular values ​​with the code basis vectors. The error rate of the qubits is used to calculate the secure key rate, and the calculation of the secure key rate does not depend on the alignment between the code basis vectors of Alice and Bob; S5: Alice and Bob, the two communicating parties, combine the code base vectors based on a secure key rate. The reserved bits are used to perform key negotiation and confidentiality enhancement, and the final security key is extracted.

[0006] To optimize the above technical solution, the specific measures also include: In step S1, the code-forming basis vector Depend on and Composition, test basis vectors Depend on and Composition, test basis vectors Depend on and The composition, wherein the quantum state is any one of the following six quantum states: Among them, 0, 1, , , and Represents quantum state symbols, subscripts It means Alice or Bob.

[0007] Further, in step S2, the third party Charlie performs Bell state projection measurement on the received quantum states. Specifically, each received quantum state is projected onto a Bell state. When Charlie's measurement result corresponds to the Bell state, the measurement is declared successful.

[0008] In step S3, the calculation of the gain and qubit error rate under the basis vector combination specifically involves: The gain represents the ratio of the number of times Charlie announced a successful measurement under this basis combination to the total number of sub-states under this basis combination sent by Alice and Bob; The bit error rate is represented by the ratio of the number of times Charlie announced a successful measurement but the encoded bits were inconsistent under this basis combination to the total number of sub-states under this basis combination sent by Alice and Bob.

[0009] In step S4, the 3×3 correlation tensor matrix is: Its elements are The specific expression is:

[0010] in, This represents the quantum state shared by both communicating parties; This represents the trace operation; and Represents the Pauli matrix. ; ; ; ; This represents the expected value.

[0011] Further, in step S4, performing singular value decomposition on the associated tensor matrix specifically involves: performing singular value decomposition on the associated tensor matrix... Performing singular value decomposition yields three singular values ​​arranged in descending order: , and The singular values ​​remain unchanged when the reference frame undergoes any unitary transformation, regardless of the reference frame chosen by Alice and Bob.

[0012] Further, in step S4, the security key rate R The calculation formula is: ; in, Represented as code basis vector sub-bit error rate, , and This represents singular values ​​arranged in descending order; This represents the binary Shannon entropy function.

[0013] As another important technical solution, the present invention also provides an implementation system for a completely reference frame-independent quantum key distribution protocol, comprising: The quantum state preparation and transmission module allows Alice and Bob, the two communicating parties, to randomly select their local mutually unbiased basis vectors and corresponding encoded bits to prepare a corresponding quantum state. The prepared quantum state is then transmitted to a third party, Charlie, via a quantum channel. The mutually unbiased basis vectors include encoded basis vectors. and test basis vectors and ; The Bell state measurement module is used by a third party, Charlie, to perform Bell state projection measurements on the received quantum states and announce the measurement results to Alice and Bob via a public channel; if the measurement is unsuccessful, the corresponding quantum state is discarded. The basis vector announcement and data partitioning module is used by Alice and Bob, the two communicating parties, to announce the successfully measured quantum state to Charlie, a third party. It publishes the basis vector information used in preparing their respective quantum states via a public channel and combines their respective bits according to the basis vector information. Divided into different datasets Alice and Bob, the two communicating parties, randomly sample a portion of bits from each dataset and calculate the gain and bit error rate of the qubits under that basis vector combination. The security analysis and key rate calculation module is used to construct a 3×3 correlation tensor matrix of the shared quantum state between the communicating parties, perform singular value decomposition on this correlation tensor matrix to obtain three singular values ​​that are independent of the choice of reference frame, and combine the singular values ​​with the code basis vectors. The error rate of the qubits is used to calculate the secure key rate, and the calculation of the secure key rate does not depend on the alignment between the code basis vectors of Alice and Bob; The key post-processing module is used by Alice and Bob, the two communicating parties, to combine the code-forming basis vectors based on a secure key rate. The reserved bits are used to perform key negotiation and confidentiality enhancement, and the final security key is extracted.

[0014] The present invention also proposes an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements a method for implementing a completely reference frame-independent quantum key distribution protocol as described above.

[0015] The present invention also proposes a computer-readable storage medium storing a computer program that enables a computer to execute an implementation method of a completely reference-frame-independent quantum key distribution protocol as described above.

[0016] Compared with the prior art, the beneficial effects of the present invention are: Existing reference frame-independent quantum key distribution protocols still implicitly require precise alignment of the code basis vectors; otherwise, security cannot be guaranteed. This invention constructs a correlation tensor matrix whose singular values ​​are independent of the choice of reference frame, so that the amount of information obtained by an eavesdropper is completely independent of the choice of reference frame. This eliminates the need for the code basis vectors of both communicating parties to be aligned, significantly reducing the dependence on real-time reference frame calibration. This enables the system to work stably in real-world environments where the reference frame is unknown, drifting, or even widely mismatched.

[0017] This invention adopts an architecture of preparation at both ends and measurement in the middle, inheriting the core security attributes of measurement device-independent quantum key distribution protocols. It can effectively resist all attacks targeting measurement devices. Combined with the characteristic of being completely reference frame independent, it achieves dual immunity against reference frame mismatch and measurement device vulnerabilities.

[0018] Since security analysis no longer relies on the alignment assumption of code basis vectors, this invention can provide a tighter security key rate limit in scenarios where the reference frame is misaligned. Compared with existing protocols, it can achieve a higher security key rate and a longer transmission distance under the same channel conditions. It can even generate a security key when the reference frame is severely mismatched, while existing protocols may become completely ineffective.

[0019] This invention eliminates the need for a high-precision real-time reference frame calibration device and complex protection or trust assumptions for the measurement equipment, thereby simplifying the system structure, reducing the difficulty of engineering implementation and deployment costs, and facilitating the large-scale application of quantum key distribution technology in real network environments. Attached Figure Description

[0020] Figure 1 : Schematic diagram of reference frame parameters on the Bloch sphere in this embodiment of the invention.

[0021] Figure 2 : Comparison of key rate variation with transmission distance when aligning code basis vectors in this embodiment of the invention.

[0022] Figure 3: Comparison of the change in eavesdropper information content with transmission distance when the code basis vectors are aligned in the embodiments of the present invention.

[0023] Figure 4 : Comparison of key rate changes with transmission distance when the code basis vectors are not aligned in the embodiments of the present invention.

[0024] Figure 5 : Comparison of the change in eavesdropper information content with transmission distance when the code basis vectors are not aligned in the embodiments of the present invention.

[0025] Figure 6 : Key rate comparison chart of the present invention and RFI-MDI-QKD under different code basis drift degrees in the embodiments of the present invention.

[0026] Figure 7 : Comparison of eavesdropper information content between the present invention and RFI-MDI-QKD under different degrees of code basis drift in the embodiments of the present invention. Detailed Implementation

[0027] The present invention will be further described in detail below through specific embodiments, but it should not be construed as limiting the scope of the subject matter of the present invention to the following embodiments. All technologies implemented based on the above content of the present invention fall within the scope of the present invention.

[0028] In some embodiments, the present invention provides a method for implementing a completely reference frame-independent quantum key distribution protocol, comprising the following steps: S1: Alice and Bob, the communicating parties, randomly select their local unbiased basis vectors and corresponding coded bits, prepare the corresponding quantum states, and send the prepared quantum states to Charlie, the third party, through a quantum channel; the unbiased basis vectors include coded basis vectors. and test basis vectors and ; In some implementations, Alice randomly selects a basis vector. One bit Prepare any one of the following quantum states Bob randomly selects a basis vector. One bit Prepare any one of the following quantum states Coding basis vectors Depend on and Composition, test basis vectors Depend on and Composition, test basis vectors Depend on and composition.

[0029] ,

[0030] , .

[0031] in, Represents the local mutually unbiased basis vectors of Alice (Bob), 0, 1, ... , , and Represents quantum state symbols, subscripts It means Alice or Bob. Indicates and Orthogonal quantum states.

[0032] S2: Charlie, a third party, performs Bell state projection measurements on the received quantum state. When Charlie's measurement result corresponds to the Bell state, the measurement is declared successful; the success or failure of the measurement result is announced to Alice and Bob via a public channel; if the measurement is unsuccessful, the corresponding quantum state is discarded. S3: Alice and Bob, the communicating parties, announce the successfully measured quantum state to Charlie, a third party. They also publish the basis vector information used in preparing their quantum states via a public channel, and divide their respective bits into different datasets according to the basis vector combinations based on the basis vector information. ,in This represents the basis vector combination information of Alice and Bob; Alice and Bob, the communicating parties, randomly sample a portion of bits from each dataset and calculate the gain and bit error rate of the qubit under that basis vector combination; In some implementations, the gain represents the gain under the basis vector combination (here denoted as...). For example, Charlie announced the number of successful measurements ( The total number of sub-states under this basis vector combination sent by Alice and Bob ( The ratio of ).

[0033] The bit error rate of a quantum bit is represented by the combination of basis vectors (here, denoted as ). For example, Charlie announced the number of times the measurement was successful but the encoded bits were inconsistent. The total number of sub-states under this basis vector combination sent by Alice and Bob ( The ratio of ).

[0034] In some implementations, the bit error rate of a quantum bit is expressed as:

[0035] S4: Construct a 3×3 correlation tensor matrix for the shared quantum state of both communicating parties. Perform singular value decomposition on the correlation tensor matrix to obtain three singular values ​​that are independent of the choice of reference frame. Calculate the secure key rate based on the singular values ​​and the bit error rate of the qubits under the code basis vectors. The calculation of the secure key rate does not depend on the alignment between the code basis vectors of Alice and Bob. The FRFI-MDI-QKD protocol for preparation and measurement is equivalently transformed into an entanglement-based protocol. Alice and Bob pre-prepared entangled states. and Preserving particles and Locally, the particles and Send to an untrusted third party, Charlie, for Bell state measurements; under this equivalent entanglement description: In some implementations... and The encoding is Alice (Bob) using code base vectors. Measuring particles ( ), and The encoding is Alice (Bob) using the test basis. Measuring particles ( ), and The encoding is Alice (Bob) using the test basis. ( ) Measuring particles ( ).

[0036] In some implementations, Alice and Bob will use local basis vectors to measure particles. and The operation was delayed until Charlie announced the particle and Following the Bell state measurement results, Alice and Bob's measurements now work together on a quantum state. This quantum state In the Pauli representation, it is represented as:

[0037] in, Represents the identity matrix. and Represents three Pauli matrices. , and Represents the local Bloch vector. , , express Correlation tensor matrix elements, This represents the trace operation; In some implementations, the 3×3 correlation tensor matrix is The expression is:

[0038] in, ; ; ; This represents the expected value.

[0039] Since the reference frame may undergo unknown unitary transformations, this invention needs to find physical quantities that are independent of the choice of reference frame, for any unitary transformation. There exists a corresponding rotation matrix. Make For quantum states Apply appropriate local unitary transformation ,get:

[0040] in, correlation tensor matrix It is a diagonal matrix. , , , Is with Corresponding rotation. In some implementations, it is assumed that... Introducing more mixed quantum states:

[0041] in, and The correlation tensor matrices are the same, but The local Bloch vector is zero. It is a Bell diagonal state.

[0042] In some implementations, by means of conduct The inverse transform yields:

[0043] in, and Since the correlation tensor matrix is ​​the same, the resulting observables are the same. .However, Compare A greater mix means that Eve, the eavesdropper, can obtain more (or at least the same) amount of information from it; In some implementations, using this hybrid state for security analysis will provide a lower bound on the actual protocol's secure key rate, ensuring it won't fall below this bound. Because... It is a Bell diagonal state, which can be rewritten as:

[0044] in, , , , ,according to The two representations yield the relation:

[0045]

[0046] In some implementations, the conditional entropy of Eve's qubits held by Bob is calculated using quantum dissociation, based on the Koashi-Winter relation [Masato Koashi, Andreas Winter. Monogamy of quantum entanglement and other correlations [J]. Physical Review A, 2004, 69:22309. DOI:10.1103 / physreva.69.022309.], yielding:

[0047] in, Represents the code basis vectors that traverse all possible projective measurements. Then, the minimum conditional entropy of Eve's measurement of Bob's result; The quantum dissociation of a Bell diagonal state is expressed as:

[0048] in, This represents the binary Shannon entropy function.

[0049] right Correlation tensor matrix Perform singular value decomposition, combined with and The relational expression yields three singular values ​​arranged in descending order: , , The singular values ​​remain unchanged under any unitary transformation of the reference frame, regardless of the reference frames chosen by Alice and Bob.

[0050] In some implementations, the secure key rate of FRFI-MDI-QKD is determined according to the Devetak-Winter limit [Igor Devetak, Andreas Winter. Distillation of secret key and entanglement from quantum states[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005, 461:207-235. DOI:10.1103 / physreva.71.062303.]. R The calculation formula is: ; ; in, Represented as code base vector sub-bit error rate; Represents the binary Shannon entropy function; this is the security key rate. R The eavesdropper information content in the calculation formula does not include any parameters related to reference frame alignment. Therefore, even if Alice and Bob's code basis vectors are not aligned, this protocol can still accurately estimate the eavesdropper information content, and thus accurately estimate the security key rate.

[0051] S5: Alice and Bob, the two communicating parties, perform key negotiation and confidentiality enhancement on the bits reserved under the combination of code basis vectors based on the security key rate, and extract the final security key.

[0052] In some embodiments, the simulation parameters adopted by the present invention are: the detection efficiency of the single-photon detector is... The dark count rate of a single-photon detector is The background bit error rate is The negotiation efficiency of reverse negotiation is Based on these parameters, the FRFI-MDI-QKD protocol was simulated, and the results are shown in the attached figure: like Figure 1 As shown, the reference frame is represented on the Bloch sphere by the polarization angle. Azimuth and the relative phase between the two calculated ground state vectors To depict; in the picture, and The code basis vectors that constitute Alice , and The code basis vectors that constitute Bob .

[0053] like Figure 2 As shown, in the case of code basis alignment (i.e.) , and Comparison of key rates and transmission distances for FRFI-MDI-QKD, RFI-MDI-QKD, and MDI-QKD under drift conditions; the key rate performance of this invention is the same as that of RFI-MDI-QKD, and neither is affected by φ and γ drift; while the key rate of MDI-QKD decreases significantly with drift, indicating that this invention can still maintain stable coding capability when there is slow drift in the reference frame.

[0054] In some implementations, such as Figure 3 As shown, in the case of code basis alignment (i.e.) , and A comparison of eavesdropper information content and transmission distance for FRFI-MDI-QKD, RFI-MDI-QKD, and MDI-QKD under drift conditions. The present invention has the same eavesdropper information content as RFI-MDI-QKD and is unaffected by drift, while the eavesdropper information content of MDI-QKD increases with drift, indicating that the present invention can effectively limit the amount of information acquired by the eavesdropper even under reference frame drift conditions.

[0055] like Figure 4 As shown, in the case where the code basis vectors are not aligned (i.e. , and The graph compares the key rate and transmission distance of FRFI-MDI-QKD, RFI-MDI-QKD, and MDI-QKD under drift conditions. The key rate performance of this invention is significantly better than both RFI-MDI-QKD and MDI-QKD, and remains unaffected by φ and γ drift. The performance of MDI-QKD continues to deteriorate, indicating that this invention has significantly higher key generation capability in real-world scenarios where the code basis vectors are not aligned.

[0056] like Figure 5 As shown, in the case where the code basis vectors are not aligned (i.e. , and A comparison of eavesdropper information content and transmission distance for FRFI-MDI-QKD, RFI-MDI-QKD, and MDI-QKD under drift conditions. In this invention, the eavesdropper acquires the lowest amount of information, unaffected by φ and γ drift; RFI-MDI-QKD is second, and MDI-QKD is the highest, increasing with drift. This indicates that this invention can more effectively suppress information leakage and provides stronger security even when the reference frame is misaligned.

[0057] like Figure 6 As shown, with the drift of the code basis vector (i.e. , and (Arbitrary drift exists). A comparison of key rates and transmission distances for FRFI-MDI-QKD and RFI-MDI-QKD. Same. The key rate of this invention is consistently superior to RFI-MDI-QKD; when At that time, the present invention can still generate codes, while RFI-MDI-QKD can no longer generate codes, proving that the present invention has extremely strong tolerance to large-angle drift of the code generation basis vector, thus expanding the practical application scenarios.

[0058] In some implementations, such as Figure 7 As shown, with the drift of the code basis vector (i.e. , and (Arbitrary drift exists). Comparison of eavesdropper information content and transmission distance for FRFI-MDI-QKD and RFI-MDI-QKD. The amount of eavesdropper information in this invention is always lower than that in RFI-MDI-QKD; with With the increase in the amount of eavesdropping information, the eavesdropping information content of the present invention remains stable, while that of RFI-MDI-QKD increases significantly. This fully demonstrates the superior security performance of the present invention in maintaining low information leakage even when the code basis vectors are misaligned.

[0059] In another embodiment, the present invention proposes an implementation system for a completely reference frame-independent quantum key distribution protocol, comprising: The quantum state preparation and transmission module allows Alice and Bob, the two communicating parties, to randomly select their local mutually unbiased basis vectors and corresponding encoded bits to prepare a corresponding quantum state. The prepared quantum state is then transmitted to a third party, Charlie, via a quantum channel. The mutually unbiased basis vectors include encoded basis vectors. and test basis vectors and ; The Bell state measurement module is used by a third party, Charlie, to perform Bell state projection measurements on the received quantum states and announce the measurement results to Alice and Bob via a public channel; if the measurement is unsuccessful, the corresponding quantum state is discarded. The basis vector announcement and data partitioning module is used by Alice and Bob, the two communicating parties, to announce the successfully measured quantum state to Charlie, a third party. It publishes the basis vector information used in preparing their respective quantum states via a public channel and combines their respective bits according to the basis vector information. Divided into different datasets Alice and Bob, the two communicating parties, randomly sample a portion of bits from each dataset and calculate the gain and bit error rate of the qubits under that basis vector combination. The security analysis and key rate calculation module is used to construct a 3×3 correlation tensor matrix of the shared quantum state between the communicating parties, perform singular value decomposition on this correlation tensor matrix to obtain three singular values ​​that are independent of the choice of reference frame, and combine the singular values ​​with the code basis vectors. The error rate of the qubits is used to calculate the secure key rate, and the calculation of the secure key rate does not depend on the alignment between the code basis vectors of Alice and Bob; The key post-processing module is used by Alice and Bob, the two communicating parties, to combine the code-forming basis vectors based on a secure key rate. The reserved bits are used to perform key negotiation and confidentiality enhancement, and the final security key is extracted.

[0060] In another embodiment of the present invention, an electronic device is proposed, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements a method for implementing a completely reference frame-independent quantum key distribution protocol as described above.

[0061] In another embodiment of the present invention, a computer-readable storage medium is provided storing a computer program that causes a computer to execute an implementation method of a completely reference-frame-independent quantum key distribution protocol as described above.

[0062] In the embodiments disclosed in this application, a computer storage medium may be a tangible medium that may contain or store programs for use by or in conjunction with an instruction execution system, apparatus, or device. The computer storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of computer storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0063] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications, equivalent substitutions, and improvements made by those skilled in the art to the above embodiments without departing from the scope of the technical solution of the present invention, based on the technical essence of the present invention, shall still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for implementing a completely reference frame-independent quantum key distribution protocol, characterized in that, Includes the following steps: S1: Alice and Bob, the communicating parties, randomly select their local unbiased basis vectors and corresponding coded bits, prepare the corresponding quantum states, and send the prepared quantum states to Charlie, the third party, through a quantum channel; the unbiased basis vectors include coded basis vectors. and test basis vectors and ; S2: Charlie, a third party, performs Bell projection measurement on the received quantum state and announces the measurement result to Alice and Bob via a public channel whether the measurement was successful; if the measurement is unsuccessful, the corresponding quantum state is discarded. S3: Alice and Bob, the communicating parties, announce the successfully measured quantum state to Charlie, a third party, and publish the basis vector information used in preparing their respective quantum states through a public channel. Based on the basis vector information, they combine their respective bits according to the basis vectors. Divided into different datasets Alice and Bob, the two communicating parties, randomly sample a portion of bits from each dataset and calculate the gain and bit error rate of the qubits under that basis vector combination. S4: Construct a 3×3 correlation tensor matrix that represents the shared quantum state between the communicating parties. Perform singular value decomposition on this correlation tensor matrix to obtain three singular values ​​that are independent of the choice of reference frame. Combine the singular values ​​with the code basis vectors. The error rate of the qubits is used to calculate the secure key rate, and the calculation of the secure key rate does not depend on the alignment between the code basis vectors of Alice and Bob; S5: Alice and Bob, the two communicating parties, combine the code base vectors based on a secure key rate. The reserved bits are used to perform key negotiation and confidentiality enhancement, and the final security key is extracted.

2. The method for implementing a completely reference frame-independent quantum key distribution protocol according to claim 1, characterized in that: In step S1, the code-forming basis vector Depend on and Composition, test basis vectors Depend on and Composition, test basis vectors Depend on and The composition, wherein the quantum state is any one of the following six quantum states: Among them, 0, 1, , , and Represents quantum state symbols, subscripts It means Alice or Bob.

3. The method for implementing a completely reference frame-independent quantum key distribution protocol according to claim 1, characterized in that: In step S2, the third party Charlie performs Bell state projection measurements on the received quantum states. Specifically, each received quantum state is projected onto a Bell state. When Charlie's measurement result corresponds to the Bell state, the measurement is declared successful.

4. The method for implementing a completely reference frame-independent quantum key distribution protocol according to claim 1, characterized in that: In step S3, the calculation of the gain and qubit error rate under the basis vector combination specifically involves: The gain represents the ratio of the number of times Charlie announced a successful measurement under this basis combination to the total number of sub-states under this basis combination sent by Alice and Bob; The bit error rate is represented by the ratio of the number of times Charlie announced a successful measurement but the encoded bits were inconsistent under this basis combination to the total number of sub-states under this basis combination sent by Alice and Bob.

5. The method for implementing a completely reference frame-independent quantum key distribution protocol according to claim 1, characterized in that: In step S4, the 3×3 correlation tensor matrix is: Its elements are The specific expression is: in, This represents the quantum state shared by both communicating parties; This represents the trace operation; and Represents the Pauli matrix. ; ; ; ; This represents the expected value.

6. The method for implementing a completely reference frame-independent quantum key distribution protocol according to claim 1, characterized in that: In step S4, performing singular value decomposition on the correlated tensor matrix specifically involves: performing singular value decomposition on the correlated tensor matrix... Performing singular value decomposition yields three singular values ​​arranged in descending order: , and The singular values ​​remain unchanged when the reference frame undergoes any unitary transformation, regardless of the reference frame chosen by Alice and Bob.

7. The method for implementing a completely reference frame-independent quantum key distribution protocol according to claim 1, characterized in that: In step S4, the security key rate R The calculation formula is: ； in, Represented as code basis vector sub-bit error rate, , and This represents singular values ​​arranged in descending order; This represents the binary Shannon entropy function.

8. A system for implementing a completely reference-frame-independent quantum key distribution protocol, characterized in that, include: The quantum state preparation and transmission module allows Alice and Bob, the two communicating parties, to randomly select their local mutually unbiased basis vectors and corresponding encoded bits to prepare a corresponding quantum state. The prepared quantum state is then transmitted to a third party, Charlie, via a quantum channel. The mutually unbiased basis vectors include encoded basis vectors. and test basis vectors and ; The Bell state measurement module is used by a third party, Charlie, to perform Bell state projection measurements on the received quantum states and announce the measurement results to Alice and Bob via a public channel; if the measurement is unsuccessful, the corresponding quantum state is discarded. The basis vector announcement and data partitioning module is used by Alice and Bob, the two communicating parties, to announce the successfully measured quantum state to Charlie, a third party. It publishes the basis vector information used in preparing their respective quantum states via a public channel and combines their respective bits according to the basis vector information. Divided into different datasets ; Alice and Bob, the two communicating parties, randomly sample a portion of bits from each dataset and calculate the gain and bit error rate of the qubits under that basis combination; The security analysis and key rate calculation module is used to construct a 3×3 correlation tensor matrix of the shared quantum state between the communicating parties, perform singular value decomposition on this correlation tensor matrix to obtain three singular values ​​that are independent of the choice of reference frame, and combine the singular values ​​with the code basis vectors. The error rate of the qubits is used to calculate the secure key rate, and the calculation of the secure key rate does not depend on the alignment between the code basis vectors of Alice and Bob; The key post-processing module is used by Alice and Bob, the two communicating parties, to combine the code-forming basis vectors based on a secure key rate. The reserved bits are used to perform key negotiation and confidentiality enhancement, and the final security key is extracted.

9. An electronic device, characterized in that, include: The present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements a method for implementing a fully reference-frame-independent quantum key distribution protocol as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: The computer program causes the computer to execute a method for implementing a fully reference-frame-independent quantum key distribution protocol as described in any one of claims 1 to 7.

Images