Quantum key distribution method and system based on full same particle exchange symmetry simulation

Abstract

The application relates to the technical field of quantum information security, and provides a quantum key distribution method and system based on exchange symmetry simulation of identical particles. Communication parties determine an initial reference state, a unitary operator and a fermion exchange operator through an authenticated channel; a sender generates random bits and encodes the random bits into the initial reference state or a negative vector thereof, performs a pseudo-state transformation through the unitary transformation, and then publicly transmits the pseudo-state; a receiver applies the fermion exchange operator to the recovered pseudo-state through inverse transformation, calculates an inner product with the initial reference state, and decodes key bits. After multiple rounds of repetition, a security key is extracted through error rate detection and privacy amplification. The application can be simulated by linear algebra on a classical computer or executed by quantum hardware, reduces deployment threshold and system complexity, and endogenously generates security through random unitary transformation and exchange symmetry of identical particles, so that the application can resist man-in-the-middle attacks and information interception.

Description

Technical Field

[0001] This application relates to the field of quantum information security technology, and more specifically, to a quantum key distribution method and system based on the simulation of identical particle exchange symmetry. Background Technology

[0002] With the rapid development of technologies such as the Internet, cloud computing, and the Internet of Things, modern information systems have placed higher demands on the security and efficiency of key distribution. Existing classical key distribution protocols (such as Diffie-Hellman) typically expose exchange parameters directly to public channels and lack embedded authentication mechanisms, making them inherently vulnerable to man-in-the-middle attacks. Even with improved solutions incorporating Public Key Infrastructure (PKI), their security heavily relies on external trust anchors such as Certificate Authorities (CAs). Once these anchors are compromised, the entire key distribution process loses all security. Furthermore, existing quantum cryptography schemes based on the symmetry of identical particle commutation largely remain at the theoretical physics level, lacking a complete protocol flow from bit generation, encoding, spoofing, transmission to decoding and measurement, and failing to provide specific algorithmic steps that can be simulated on classical computers, resulting in high experimental barriers and low practical applicability. Existing technologies struggle to balance low-complexity deployment with inherent security and are unable to effectively counter increasingly sophisticated and persistent cyberattacks.

[0003] To address the aforementioned issues, existing technologies urgently need improvement. Summary of the Invention

[0004] The purpose of this application is to provide a quantum key distribution method and system based on the simulation of identical particle exchange symmetry. It has the advantages of enabling secure key negotiation on a classical computer without the need for real quantum hardware, and endowing the protocol with intrinsic security through unitary transformation masquerading and identical particle exchange symmetry, effectively resisting information interception and man-in-the-middle attacks.

[0005] In a first aspect, this application provides a quantum key distribution method based on the simulation of identical particle exchange symmetry, including: The two communicating parties establish a connection through an authenticated channel and negotiate to determine the initial reference state, unitary operator, and fermion commutation operator; The sender generates random bits. When the random bits have a first value, the initial reference state is used as the sending state. When the random bits have a second value, the fermion commutation operator is applied to the initial reference state once to obtain the sending state. The sender uses the unitary operator to perform a unitary transformation on the transmitted state to obtain a masquerading state, and then transmits the masquerading state to the receiver through a public channel. The receiver uses the inverse transform of the unitary operator to recover the received dummy state, thus obtaining the recovered state; The receiver applies the fermion exchange operator to the recovered state, calculates the inner product of the applied state and the initial reference state, and decodes the key bit corresponding to the random bit based on the value of the inner product to complete the distribution of the quantum key in this round.

[0006] Furthermore, the initial reference state is a joint state of two particles with spin-up, represented by a complex vector in a direct product basis.

[0007] Furthermore, the unitary operator is a complex unitary matrix acting on the Hilbert space where the initial reference state is located, and its inverse transformation is the conjugate transpose of the unitary operator. The two communicating parties synchronize the unitary operator through an authenticated channel, and different sessions use different unitary operators. The fermion exchange operator is a matrix operator obtained by taking the negative of the standard two-particle state exchange operator.

[0008] Furthermore, when the random bit is a first value, the transmitting state is equal to the initial reference state; when the random bit is a second value, the transmitting state is the state after applying the fermion commutation operator to the initial reference state; the transmitting state is the initial reference state or its negative vector.

[0009] Furthermore, the masquerading state is the product of the unitary operator and the transmitting state; the receiver applies the inverse transformation of the unitary operator to the masquerading state to obtain the recovered state.

[0010] Furthermore, the receiver applies the fermion commutation operator to the recovered state, and then the method further includes: Calculate the inner product of the initial reference state and the recovered state after application; when the inner product is of the first polarity, the decoded key bits are the first value; when the inner product is of the second polarity, the decoded key bits are the second value; when the inner product does not satisfy the first polarity or the second polarity, the receiver marks this round of transmission as invalid and requests a retransmission from the sender through the authenticated channel.

[0011] Furthermore, the method also includes: The two communicating parties negotiate and determine the number of session rounds, and repeatedly execute the process of the sender generating random bits and the receiver decoding key bits to obtain a multi-bit raw key; During the multi-round transmission process, after the sender completes the previous round of transmission in the masquerade state and receives the acknowledgment signal from the receiver, it starts the generation and encoding of the next round of random bits. Before each round of transmission, the current round number and synchronization information are attached to the masquerade state and transmitted together. The two communicating parties compare the random bits generated by the sender with the key bits decoded by the receiver in at least some rounds through an authenticated channel to calculate the bit error rate. If the bit error rate is lower than a preset threshold, privacy amplification is performed on the key bits in the remaining rounds to extract the final security key.

[0012] Furthermore, the method is simulated and executed on a classical computer using linear algebra operations, wherein the quantum state is represented by a complex vector, the unitary transform, the inverse transform, and the fermion commutation operator are all represented by complex matrices, and the inner product is implemented through vector inner product operations.

[0013] Furthermore, the method is executed on quantum hardware: Two qubits are allocated on the quantum processor and initialized to the initial reference state. The unitary transform and the inverse transform are implemented by applying a quantum gate sequence to the two qubits. The dummy state is transmitted through a quantum channel. The inner product is obtained by measuring the overlap probability between the recovered state after applying the fermion commutation operator and the initial reference state.

[0014] Secondly, this embodiment also provides a quantum key distribution system based on the simulation of identical particle exchange symmetry, for performing the method described in the first aspect, including: The initialization module is used by the two communicating parties to establish a connection through an authenticated channel and negotiate and determine the initial reference state, unitary operator, and fermion commutation operator. The encoding module is used by the sender to generate random bits. When the random bits are of a first value, the initial reference state is used as the transmission state. When the random bits are of a second value, the fermion commutation operator is applied to the initial reference state once to obtain the transmission state. The camouflage and transmission module is used by the sender to perform a unitary transformation on the transmitted state using the unitary operator to obtain a camouflage state, and then transmits the camouflage state to the receiver through a public channel. The recovery module is used by the receiver to recover the received dummy state by using the inverse transformation of the unitary operator to obtain the recovered state; The decoding module is used by the receiver to apply the fermion exchange operator to the recovered state, calculate the inner product of the applied state and the initial reference state, and decode the key bit corresponding to the random bit according to the value of the inner product, so as to complete the distribution of the quantum key in this round.

[0015] As can be seen from the above, this embodiment solves the problems of existing key distribution protocols lacking intrinsic security, having high system complexity, and being difficult to apply quantum cryptography schemes in classical environments by incorporating key information into the number of identical particle swaps and transmitting it in disguise through random unitary transformation, combined with the inner product measurement decision mechanism. It has the advantages of being able to complete key security negotiation without real quantum hardware, reducing system complexity and deployment threshold, and endowing the protocol with intrinsic security through random unitary transformation and identical particle swap symmetry, effectively resisting man-in-the-middle attacks and information interception. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating the steps of the quantum key distribution method based on the simulation of identical particle exchange symmetry disclosed in the embodiments of this application; Figure 2 This is a schematic diagram of the quantum key distribution system structure based on the simulation of identical particle exchange symmetry disclosed in the embodiments of this application; Figure 3 This is a schematic diagram of the system structure of another quantum key distribution system based on the simulation of identical particle exchange symmetry disclosed in the embodiments of this application; Figure 4 This is a schematic diagram of the execution flow of another quantum key distribution system based on the simulation of identical particle exchange symmetry disclosed in this application. Detailed Implementation

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which these embodiments belong; the terminology used herein and in the specification of the application is for the purpose of describing particular embodiments only and is not intended to limit these embodiments; the terms "comprising" and "having," and any variations thereof, in the specification of these embodiments and the foregoing drawings, are intended to cover non-exclusive inclusion. The terms "first," "second," etc., in the specification of these embodiments and the foregoing drawings are used to distinguish different objects, not to describe a particular order.

[0019] The implementation details of the technical solution in this embodiment are described in detail below: This application proposes a quantum key distribution method based on the simulation of identical particle exchange symmetry, such as... Figure 1 As shown, the method includes: S101, the two communicating parties establish a connection through the authenticated channel and negotiate to determine the initial reference state, unitary operator, and fermion commutation operator.

[0020] In this embodiment, Alice and Bob first establish a connection through an authenticated secure classic channel, which employs a secure transmission platform with two-way authentication. After the connection is established, both parties perform two-way authentication to verify each other's identities and prevent man-in-the-middle attacks. After successful authentication, both parties negotiate and determine the core parameters required for this key distribution session, including the initial reference state, unitary operator, and fermion exchange operator, establishing a unified mathematical framework and protocol benchmark for subsequent encoding, spoofing, transmission, and decoding processes.

[0021] Furthermore, the initial reference state is a joint state of two particles with spin-up, represented by a complex vector in a direct product basis.

[0022] Specifically, this embodiment uses a two-particle spin system to simulate identical fermions, considering two identical fermions, each with a two-level degree of freedom (e.g., spin 1 / 2, spin up). Or spin downward In classical simulations, the initial reference state is represented by a 4-dimensional complex vector, with the basis vectors being a direct product basis:

[0023] That is, the basis vectors are in sequence as follows The initial state is then fixed as follows:

[0024] This state This indicates that both fermions have their spins up, serving as their respective initial states. Each fermion stores a digital representation of this reference state locally, which serves as the basis for all subsequent inner product calculations and judgments.

[0025] Furthermore, the unitary operator is a complex unitary matrix acting on the Hilbert space where the initial reference state is located, and its inverse transformation is the conjugate transpose of the unitary operator. The two communicating parties synchronize the unitary operator through an authenticated channel, and different sessions use different unitary operators. The fermion exchange operator is a matrix operator obtained by taking the negative of the standard two-particle state exchange operator.

[0026] Specifically, the unitary operator U is one of the core security elements of this communication. U is a 4×4 unitary matrix acting on the entire two-particle four-dimensional Hilbert space, satisfying... During the initialization phase, Alice and Bob select the specific form of U through classic channel negotiation. Furthermore, U can be changed during each session to enhance long-term security. The design principle of U is: for any input state... The result obtained after U-transformation Under standard computational basis, it will appear as a superposition of four complex amplitudes, without any recognizable pattern.

[0027] In practice, either or both communicating parties invoke a cryptographically secure pseudo-random number generator to produce a new high-entropy random seed. Based on this random seed, a unitary 4×4 complex matrix is ​​regenerated as U for the current session, and this matrix is ​​resynchronized and updated via the authenticated channel during the next session initialization. This module also calculates the inverse matrix U† (i.e., the conjugate transpose) of U. Since U†U = I, U† is the inverse transformation of U.

[0028] Furthermore, the fermion commutation operator is a matrix operator obtained by negating the standard two-particle state commutation operator. Specifically, the standard commutation operator SWAP is defined, which swaps the states of two particles:

[0029] The matrix representation under the direct product basis is as follows:

[0030] The matrix will and Interchange, while maintaining and The commutative antisymmetry of identical fermions is defined as follows: commutating two fermions reverses the sign of the global wavefunction. Therefore, the fermion commutation operator used in the simulation is defined as:

[0031] Obviously, S f 2 =( SWAP 2 =SWAP 2 =I, and S f It is a unitary matrix (S f † S f =I). When this operator acts on any two fermion states, it not only swaps the particle positions but also introduces a global negative sign, thus accurately simulating the behavior of identical fermions. In subsequent encoding steps, Alice will utilize S f Perform operations on the initial state, encoding the key bits as... or .

[0032] S102, the sender generates a random bit. When the random bit is a first value, the initial reference state is used as the sending state. When the random bit is a second value, the fermion commutation operator is applied to the initial reference state once to obtain the sending state.

[0033] In this embodiment, the data encoding module on the Alice side begins to work, first calling a classic random number generator to generate a uniformly distributed random bit. This bit serves as one bit of the original key. Alice then encodes the key bit k as a pair of bits for the initial state. Applying the fermion commutation operator S f The specific rules for the number of times are as follows: If k=0, then send state ; If k=1, then send state ; because And SWAP = Therefore, the sending state can be uniformly written as: .

[0034] Furthermore, when the random bit is a first value, the transmitting state is equal to the initial reference state; when the random bit is a second value, the transmitting state is the state after applying the fermion commutation operator to the initial reference state; the transmitting state is the initial reference state or its negative vector.

[0035] In this embodiment, if k=0 (i.e., the first value), then the sending state is... = = If k=1 (i.e., the second value), then the sending state... = = - Since applying the Sf operation only introduces a global negative sign and does not change the physically observable properties of the state, but uses this global phase information as the carrier of the key bits, the transmitted state is mathematically strictly confined to a one-dimensional subspace spanned by the initial reference state; that is, the transmitted state can only be... or One of these two methods ensures that the encoded quantum state carries only a single bit of key information and provides a clear mathematical basis for the subsequent receiver to recover the key through the inner product positive and negative decision.

[0036] S103, the sender uses the unitary operator to perform a unitary transformation on the transmitted state to obtain a masquerading state, and transmits the masquerading state to the receiver through a public channel.

[0037] Furthermore, the masquerading state is the product of the unitary operator and the transmitting state; the receiver applies the inverse transformation of the unitary operator to the masquerading state to obtain the recovered state.

[0038] Specifically, in this embodiment, the encoded transmission state Before entering the public channel, a pre-negotiated unitary operator U is applied through the appearance transformation module to generate a dummy state. This dummy step is the core of the protocol's secure transmission, aiming to protect the quantum state during transmission through the public channel, prevent eavesdroppers from directly reading the encoded information, and make the transmitted information difficult for attackers to effectively intercept.

[0039] Furthermore, the masquerading state is the product of the unitary operator and the sending state. Specifically, the masquerading state is determined by the following formula:

[0040] Since U is randomly selected from a 4×4 unitary matrix, and no one except Alice and Bob knows it, therefore The representation under the standard computational basis would appear as a random superposition of four complex amplitudes, with no discernible pattern. For Eve, the eavesdropper unaware of U, interception... Subsequently, regardless of the measurement standard she used for observation, the results were like random noise, making it impossible to infer anything. What exactly is it? still- Therefore, it is impossible to obtain the key bit k.

[0041] because After transformation The first column. Since U is a 4×4 unitary matrix acting on the four-dimensional Hilbert space of the two particles, and its specific form is unknown to anyone except Alice and Bob, therefore The representation under the standard computational basis would appear as a random superposition of four complex amplitudes, with no discernible pattern. For Eve, the eavesdropper unaware of U, interception... Subsequently, regardless of the measurement standard she used for observation, the results were like random noise, making it impossible to infer anything. What exactly is it? still- Therefore, the key bit k cannot be obtained. The disguised state presents a random distribution with equal amplitude for each component under the standard basis, which cannot be directly deciphered by the eavesdropper.

[0042] Subsequently, disguise The quantum state is transmitted to Bob's end via a public channel. During this process, any eavesdropper intercepting it will only receive a disguised quantum state. Since the eavesdropper does not know the specific form of U, even if... Even with a complete state tomography, only random complex amplitudes can be obtained; the original transmitting state cannot be deduced. still Therefore, it is impossible to obtain the key bit k.

[0043] Furthermore, the receiver applies the inverse transformation of the unitary operator to the masquerading state to obtain the recovered state. The Bob end receives the masquerading state. Then, it is immediately imported into the inverse transform module. This module applies an inverse unitary transform based on the U parameters synchronized with Alice during the initialization phase. In this embodiment, U is a real orthogonal matrix. The recovered state is calculated. In an ideal situation, The receiver thus obtains a transmitted state that is completely identical to the sender's encoded state, laying the foundation for subsequently applying the fermion commutation operator and calculating the inner product to decode the key bits.

[0044] S104, the receiver uses the inverse transformation of the unitary operator to recover the received dummy state and obtain the recovered state.

[0045] In this embodiment, Bob receives the spoofed state transmitted via a public channel. Then, it is immediately imported into the local inverse transform module. This module applies an inverse unitary transform U† to the received dummy state based on the unitary operator U parameter synchronized with Alice through the authenticated channel during the initialization phase, thereby restoring the quantum state after random unitary transform ambiguity to the encoded original transmitted state, so as to perform subsequent fermion exchange operator operations and inner product measurements.

[0046] Specifically, the inverse transform module performs the following operations to obtain the recovered state: .

[0047] Among them, U † Let U be the conjugate transpose of the unitary operator U, which is also the inverse matrix of U, satisfying U † U = I. Due to the camouflage state By the sending end Therefore, the receiver can mathematically cancel the unitary transformation effect of the transmitter by left-multiplying by U†, so that the quantum state returns to the original encoded form.

[0048] Furthermore, in this embodiment, if the unitary operator U selected through negotiation is a real orthogonal matrix, then its inverse transformation U† is equal to its transpose matrix U The recovered state is calculated as follows: .

[0049] Under ideal eavesdropping-free and noise-free channel conditions, the recovery state The sent state is strictly equal to the Alice-encoded state. ,Right now This ensures that the receiver obtains the same quantum state as the sender, providing the necessary state basis for subsequently applying the fermion commutation operator and calculating the inner product to accurately decode the key bits.

[0050] S105, the receiver applies the fermion exchange operator to the recovered state, calculates the inner product of the applied state and the initial reference state, and decodes the key bit corresponding to the random bit according to the value of the inner product to complete the distribution of the quantum key in this round.

[0051] Specifically, in this embodiment, the Bob end obtains the recovery state. Then, inner product measurement and key decoding began. First, Bob measured the recovered state... Apply the fermion commutation operator S again f To obtain the intermediate state:

[0052] Bob then calculates the intermediate state. Reference state with local storage The inner product of the two random bits is calculated, and the key bit k′ is decoded based on the polarity decision of this inner product. This decision rule has a clear physical meaning: the sign of the inner product directly reflects whether the recovered state has an additional global negative sign relative to the reference state, and this negative sign is introduced by the Sf operation applied by Alice. In the absence of interference, the decoded key bit k′ is consistent with the random bit k generated by the sender, thus completing the secure distribution of this round of single-bit quantum key.

[0053] Furthermore, the receiver applies the fermion exchange operator to the recovered state, and then the method further includes: calculating the inner product of the initial reference state and the recovered state after application; when the inner product is of a first polarity, the decoded key bits are the first value; when the inner product is of a second polarity, the decoded key bits are the second value; when the inner product does not satisfy the first polarity or the second polarity, the receiver marks the current round of transmission as invalid and requests a retransmission from the sender through the authenticated channel.

[0054] Specifically, Bob calculates Reference state with local storage Inner product:

[0055] This inner product is mathematically equal to and The dot product is calculated as follows: because:

[0056] so:

[0057] then:

[0058] because It is normalized m is a complex number. Therefore, all operations preserve the state in a 1-dimensional subspace. Therefore, m is a real number, and it is either +1 or -1, with an imaginary part of zero.

[0059] Specifically: when k=0, m = (-1) {0+1} = -1; when k=1, m = (-1) {1+1} = +1.

[0060] The inner product calculation described above is implemented in classical simulations through vector dot products. Accurate calculations are performed using the locally stored reference state conjugate transpose vector and intermediate state vector to ensure the numerical reliability of the inner product result.

[0061] Bob decodes the key bit k′ according to the following decision rule: if the calculated inner product m = +1, then output k′ =1; if the calculated inner product m = -1, then output k′ = 0.

[0062] Based on the above derivation, under interference-free conditions, k′ = k, thus achieving consistent key generation between the two parties. This decision rule has a clear physical meaning: the sign of m directly reflects whether the recovered state has an additional global negative sign compared to the reference state, and this negative sign is precisely the S applied by Alice. f This is introduced by the operation (i.e., k=1). If the real part of the inner product m is neither +1 nor -1 due to channel noise or eavesdropping interference, Bob's k-value judgment module considers this round of transmission untrustworthy, outputs an invalid flag, the state storage module marks this round of transmission as invalid, and requests a retransmission from the sender through the authenticated channel to ensure the integrity and correctness of the finally generated key.

[0063] Furthermore, the method also includes: the two communicating parties negotiate and determine the number of session rounds, repeatedly executing the process of the sender generating random bits to the receiver decoding key bits to obtain a multi-bit original key; during the multi-round transmission process, after the sender completes the previous round of transmission in a disguised state and receives the receiver's confirmation signal, the sender starts the generation and encoding of random bits for the next round, and before each round of transmission, the current round number and synchronization information are attached to the disguised state and transmitted together; the two communicating parties compare the random bits generated by the sender and the key bits decoded by the receiver in at least some rounds through an authenticated channel, calculate the bit error rate, and if the bit error rate is lower than a preset threshold, privacy amplification is performed on the key bits of the remaining rounds to extract the final security key.

[0064] Specifically, in this embodiment, to generate a key of sufficient length, the single-bit transmission process described above needs to be repeated for a total of n rounds. In each round, Alice independently generates a new random bit ki, constructs a corresponding transmission state based on this bit value, and sequentially goes through spoofing, transmission, recovery, measurement, and decoding. Bob then obtains the corresponding decoded bit k′i. Under ideal channel and no eavesdropping conditions, after n rounds, both parties will have the exact same n-bit original key. The protocol state machine module is responsible for controlling the entire n-round cycle: from round 1 to round n, each round sequentially triggers Alice's encoding transmission and Bob's receiving measurement, and maintains a round counter to ensure that each step of the protocol is executed in the correct order, triggering corresponding error handling in abnormal situations.

[0065] In continuous multi-round transmissions, Alice's transmission control module controls the timing and rate of transmission according to the instructions of the protocol state machine. It waits for the previous round of masquerading state transmission to complete and receives an acknowledgment signal from Bob before initiating the next round of encoding and transmission. This module is also responsible for appending the current round number and necessary synchronization information (such as a timestamp) to the representation data of the masquerading state before each round of transmission. This ensures that the receiver can correctly align the recovered states received from multiple rounds based on the round number and synchronization timestamp, preventing round misalignment due to network delays or out-of-order transmission, and ensuring the accuracy of sequentially concatenating the key bits from multiple rounds.

[0066] When both parties are deployed in a real quantum hardware environment, after n rounds of initial key generation, they randomly select bits from a subset of rounds through a certified classical channel for public comparison to estimate the channel error rate. If the calculated error rate is lower than a preset security threshold, it indicates that the channel quality meets the requirements for secure communication. The parties then perform privacy amplification on the remaining uncompared key bits, using information theory methods to compress the amount of information an eavesdropper might obtain, thereby extracting the final secure key. This final secure key can be used for subsequent cryptographic applications such as data encryption, authentication, and integrity verification, providing a trust anchor for real-time secure communication in large-scale dynamic environments such as the Internet, cloud computing, and the Internet of Things.

[0067] Furthermore, the method is simulated and executed on a classical computer using linear algebra operations, wherein the quantum state is represented by a complex vector, the unitary transform, the inverse transform, and the fermion commutation operator are all represented by complex matrices, and the inner product is implemented through vector inner product operations.

[0068] In this embodiment, the entire quantum key distribution protocol is deployed on one or more high-performance computing servers interconnected by a network. These servers are equipped with multi-core central processing units, large-capacity memory, and high-speed solid-state drives, and simulate the state evolution and measurement process in quantum mechanics in a purely software manner.

[0069] The quantum simulation layer, as the core support layer running on a classical computer, is responsible for simulating the evolution, transformation, and measurement of quantum states using linear algebra operations. This layer abstracts quantum states as complex vectors and unitary operators as complex matrices, implementing operations such as matrix-vector multiplication and inner product. The state vector repository provides functions for creating, reading, updating, and deleting four-dimensional complex vectors. Internally, it maintains a memory pool to store various quantum states generated during protocol execution, including fixed reference states, encoded transmit states, disguised states, received and recovered states, and intermediate states after applying fermion commutation operators. Each state vector has a unique identifier and reference count, supporting deep copying to ensure that multiple operation modules do not interfere with each other.

[0070] The unitary operator pool pre-stores various unitary operators required during protocol execution, storing these operators in matrix form. This primarily includes random unitary operators U and their inverses U† loaded from the key management layer, fixed fermion exchange operators Sf, and provides an interface for multiplying operators with state vectors. The unitary transformation is implemented through matrix-vector multiplication of the complex matrix corresponding to the unitary operator and the complex vector representing the quantum state; the inverse transformation is implemented through matrix-vector multiplication of the inverse matrix of the unitary operator and the dummy state vector; and the fermion exchange operator is implemented through matrix-vector multiplication of its corresponding complex matrix and the recovered state vector.

[0071] The measurement calculator implements the measurement operations in the protocol, primarily inner product measurements. Specifically, the measurement calculator accepts two state vectors as input and calculates their dot product: ψ|φ = Σ_i ψ_i^* φ_i Returns a complex number result. In the ideal simulation, this calculation is an exact floating-point operation. The output of this module is directly used to determine the key bit: if the real part of the calculation result is +1, then key bit 1 is decoded; if the real part is -1, then key bit 0 is decoded; otherwise, the current round of transmission is marked as invalid. Through the exact simulation of the above linear algebraic operations, this embodiment can completely reproduce the entire quantum key distribution process based on the symmetry of identical particle exchange on a classical computer without the need for real quantum hardware, greatly reducing the experimental threshold and deployment cost.

[0072] Furthermore, the method is executed on quantum hardware: two qubits are allocated on a quantum processor and initialized to the initial reference state. In this alternative embodiment, when both communicating parties possess a programmable quantum computer or quantum communication device, such as a quantum processor based on an ion trap or superconducting qubit system, this method can run directly on quantum hardware without relying on linear algebraic simulations on a classical computer, thus becoming a complete, eavesdrop-resistant quantum key distribution protocol. Specifically, two physical qubits are allocated on the quantum processor and initialized to a two-particle spin-up joint state, such as in a quantum computing base. This state corresponds to the initial reference state in classical simulation. = This serves as the reference quantum state for the quantum key distribution protocol between the two parties.

[0073] The unitary transformation and its inverse transformation are implemented by applying a sequence of quantum gates to the two qubits. Specifically, the unitary matrix U, pre-shared by both communicating parties, is decomposed into a combination sequence of single-qubit gates and two-qubit gates according to quantum computing principles. After encoding, Alice applies this sequence of quantum gates to the two qubits sequentially, causing the quantum state to evolve from the encoded transmit state to the dummy state. After receiving the qubits, Bob applies the inverse sequence corresponding to U†, which is composed of a combination of quantum gates corresponding to the conjugate transpose of U. This inverse sequence is applied to the received quantum state to recover the original encoded state, i.e., the initial reference state or its global negative phase state.

[0074] The camouflaged state is transmitted via a quantum channel. Specifically, the camouflaged state, after unitary transformation, is sent to the receiver in the form of a physical quantum state through a quantum channel or quantum network. This quantum channel uses physical carriers such as photons, ions, or superconducting coupling to transmit quantum information, rather than transmitting complex vector data through a classical network. Any eavesdropper attempting to intercept the physical quantum state in the quantum channel will inevitably introduce a disturbance, which will be detected by both communicating parties through subsequent bit error rate detection.

[0075] The inner product is obtained by measuring the overlap probability between the recovered state after applying the fermion commutation operator and the initial reference state. Specifically, Bob applies the quantum gate operation corresponding to the fermion commutation operator Sf to the two recovered qubits. This operation can be implemented by combining SWAP gates and Z gates to simulate the antisymmetric commutation of identical fermions at the physical level. Subsequently, Bob measures the quantum state after applying this operation and the initial reference state. The overlap probability is calculated. Since the measurement results of real quantum hardware are probabilistic outputs, Bob obtains this overlap probability through repeated measurements. When the probability approaches 1, the decoded key bit is determined to be the second value; when the probability approaches 0, the decoded key bit is determined to be the first value, thus completing the inner product measurement and key decoding at the quantum level.

[0076] Because real quantum channels are susceptible to noise and eavesdropping, the communicating parties need to perform additional security enhancement steps: randomly select bits from a subset of rounds for public comparison to estimate the channel error rate; if the error rate is below a preset threshold, then privacy amplification is performed on the key bits for the remaining rounds to extract the final secure key. Compared to traditional protocols such as BB84, this method offers advantages such as simple phase encoding and no need for random selection of measurement bases, providing a highly secure and feasible path for the practical application of quantum key distribution.

[0077] Compared with existing technologies, the quantum key distribution system based on the simulation of identical particle exchange symmetry provided in this application brings the following significant advantages: (1) A complete key negotiation mechanism has been constructed. Existing quantum cryptography research based on the statistical properties of identical particles mostly remains at the theoretical physics level, lacking an end-to-end executable process from bit generation, encoding, spoofing, transmission to decoding and measurement. This application creatively integrates the antisymmetry of identical fermions into the key distribution protocol: defining a clear initial state. The explicit matrix form of the fermion commutation operator Sf, the encoding rule based on the global phase (-1)k, the camouflage mechanism based on the random unitary transform U, and the inner product-based... The decision-making criteria. This mechanism enables both communicating parties to complete key negotiation through defined operational steps, provided they have authenticated their respective identities, thus offering a novel and complete protocol paradigm for the field of quantum key distribution.

[0078] (2) Enhanced inherent security of the system. This application improves the inherent security capabilities of the key distribution system. The state transmitted in the public channel is disguised by a random unitary transformation U. Instead of the original encoded state, because U is only known to the two communicating parties and can be updated during the session, even if an eavesdropper intercepts a large amount of data... It is also impossible to deduce the original sending state. still Therefore, it is impossible to obtain the key bit k. Meanwhile, this application encodes the key information onto a joint state of two identical fermions. The encoded two states... and With an identical matrix, any eavesdropper measuring only a single particle cannot extract any information about k from it. This is a natural defense capability that single-particle coding protocols do not possess, making them more robust.

[0079] (3) Reduced system complexity. Compared with existing quantum key distribution protocols, this application significantly reduces system complexity in multiple dimensions. At the protocol execution level, the post-processing workload is greatly reduced. The entire protocol can be accurately simulated on a classical computer using linear algebra operations, requiring only 4-dimensional complex vectors and 4×4 matrix operations, with extremely low computational resource requirements. At the deployment and integration level, the modular design (transmission encryption subsystem, data encoding subsystem, and functional support subsystem) allows the system to run purely in software or be smoothly migrated to real quantum devices. It is also compatible with classical error correction and privacy amplification processes and seamlessly integrates with existing key management infrastructure, providing a low-threshold, highly secure, and feasible path for the practical application of quantum key distribution.

[0080] Secondly, this embodiment also provides a quantum key distribution system based on the simulation of identical particle exchange symmetry, such as... Figure 2 As shown, it includes: The initialization module 201 is used for the two communicating parties to establish a connection through an authenticated channel and negotiate and determine the initial reference state, unitary operator, and fermion commutation operator. The encoding module 202 is used by the sender to generate random bits. When the random bits are of a first value, the initial reference state is used as the transmission state. When the random bits are of a second value, the fermion commutation operator is applied to the initial reference state once to obtain the transmission state. The camouflage and transmission module 203 is used by the sender to perform a unitary transformation on the transmitted state using the unitary operator to obtain a camouflage state, and to transmit the camouflage state to the receiver through a public channel; Recovery module 204 is used by the receiver to recover the received dummy state using the inverse transformation of the unitary operator to obtain the recovered state; The decoding module 205 is used by the receiver to apply the fermion exchange operator to the recovered state, calculate the inner product of the applied state and the initial reference state, and decode the key bit corresponding to the random bit according to the value of the inner product, so as to complete the distribution of the quantum key in this round.

[0081] This system can be used to perform the quantum key distribution method based on the simulation of identical particle exchange symmetry described in the first aspect, which will not be elaborated further here.

[0082] Furthermore, this embodiment proposes another implementation method for a quantum key distribution system based on the simulation of identical particle exchange symmetry. Based on the principle of identical particle exchange symmetry in quantum mechanics, supported by a secure transmission platform, and designed with a layered modular architecture, a complete key distribution system from the user interface to the underlying hardware is constructed. The system adopts a five-layer architecture, from top to bottom: application layer, key management layer, quantum protocol layer, quantum simulation layer, and hardware layer. Data interaction and control coordination between layers are achieved through standardized interfaces, realizing high cohesion and low coupling of the system, facilitating functional expansion and hardware migration. The overall system architecture is as follows: Figure 3 As shown, the system operation process is as follows: Figure 4 As shown.

[0083] Regarding the system architecture, the following is included: I. Application Layer The application layer, located at the top layer of the system, directly faces users and administrators, and is responsible for encapsulating the underlying key distribution capabilities into easy-to-use business functions. This layer shields users from the quantum protocol and underlying hardware details, providing a simple operating interface. This layer comprises the following three modules: (1) User Interface Module. This module provides a command-line interface and a user interface, allowing operators to initiate key distribution sessions, view system status, configure operating parameters, and monitor real-time logs. Users can input the parameters required for this key distribution through this module, such as the number of session rounds n and the desired key length. The user interface module is also responsible for displaying the session progress (such as the number of completed rounds / total number of rounds) and the final generated key, facilitating user verification. In the event of an error or eavesdropping alarm, this module will display a prompt message and guide the user to reinitialize or adjust the parameters.

[0084] (2) Parameter Management Module. This module is responsible for managing various configuration parameters related to this key distribution session, including the identity identifiers of both communicating parties, the number of session rounds n, and other specific parameters. Before the session starts, the parameter management module receives these parameters from the user interface module, performs legality verification, and then distributes the normalized parameters to the lower layers (key management layer and quantum protocol layer). After the session ends, this module collects the execution results and sends them back to the user interface module for display or logging.

[0085] (3) Key Export / Storage Module. After successful protocol execution, this module is responsible for exporting the final generated security key in a specified format (such as hexadecimal string, Base64 encoding, or binary file), and can optionally store it on a local secure storage medium. Before exporting, this module compares the key with the checksum exchanged between the communicating parties to ensure that the keys are consistent and have not been tampered with. This module also provides key lifecycle management functions, such as key archiving, version marking, and expiration destruction, to support secure calls from upper-layer applications (such as VPN encryption, disk encryption, and message authentication).

[0086] II. Key Management Layer The key management layer is the core control center of the entire system, responsible for all management functions related to key generation, transformation, and security parameters. This layer does not directly handle quantum states, but rather provides the necessary key materials and operator definitions for upper-layer protocols. It ensures the confidentiality and consistency of all encryption parameters (especially the unitary operator U). This layer comprises the following three modules: (1) Random Number Management Module. This module is responsible for providing a random number source for the system, satisfying the cryptographic requirement of unpredictability. Its specific responsibilities include: generating the key bits k required for Alice encoding (each bit is independently and uniformly randomized), and generating the random seed required for the unitary operator U in the initialization phase. The random number management module can interface with various random number sources: the cryptographically secure pseudo-random number generator provided by the operating system or random number algorithms approved by the State Cryptography Administration.

[0087] (2) Unitary Operator Definition Module. This module is responsible for the generation, storage, and distribution of the unitary operator U and its inverse U† in the corresponding method. During the session initialization phase, this module calls the random number management module to obtain a high-entropy random seed and randomly generates a 4×4 complex unitary matrix U (satisfying U†U = I). This module also calculates the inverse matrix U† of U (i.e., the conjugate transpose). Subsequently, U is encrypted and synchronized to the corresponding module at the communication peer through a secure transmission platform to ensure that both parties obtain the exact same U.

[0088] (3) Commutation Operator Definition Module. This module stores the 4×4 matrix representation of the fermion commutation operator Sf = -SWAP, as well as the initial reference state. The four-dimensional complex vector representation. These parameters form the mathematical basis for protocol encoding and decoding, are session-independent, are loaded into memory during system initialization, and remain unchanged throughout runtime. The specific form of the Sf matrix is: -1 in all positions except the second and third positions on the main diagonal, and -1 in the corresponding positions on the secondary diagonal. Initial reference state The vector representation is [1,0,0,0]T (in the direct product basis). (See below). This module provides a read-only interface for use by the encoding and inner product calculation modules in the quantum protocol layer.

[0089] III. Quantum Protocol Layer The quantum protocol layer implements the complete logical flow of the key distribution method described in this application, including the protocol behavior of Alice and Bob, quantum state transmission control, and state machine management. This layer completes state operations by calling the interface of the lower layer (quantum simulation layer). Specifically: (1) Alice Protocol Logic Module. This module implements all protocol actions of the sender and includes the following sub-modules: a) Key Encoding Module: This submodule is responsible for encoding the single-bit key k into a quantum state. It obtains a random bit k∈{0,1} from the random number management module of the key management layer, and then constructs the transmission state according to the encoding rules. Specifically, if k=0, then the transmission state... Equal to the initial reference state obtained from the commutation operator definition module If k=1, then the sending state This module outputs a four-dimensional complex vector. Meanwhile, the k value is temporarily stored in local memory for later comparison with Bob.

[0090] b) Unitary conversion module: This submodule receives the output from the key encoding module. It also obtains the unitary operator U of the current session from the unitary operator definition module of the key management layer and calculates the masquerading state. .because Only or Therefore This is actually equal to the first column of ±U. The output of this module is a camouflaged state, which is also a four-dimensional complex vector. The core function of this module is to make the original coded state completely unrecognizable under the standard basis, thereby achieving active concealment at the transport layer.

[0091] c) Transmission Control Module: This submodule is responsible for transmitting the masquerading state. The transmission module is responsible for sending the data. It controls the timing and rate of transmission according to the instructions of the protocol state machine. For example, in multiple consecutive transmission rounds, the transmission control module waits for the previous round to complete and receives Bob's acknowledgment signal before starting the next round of encoding and transmission. This module is also responsible for transmitting the current round number and necessary synchronization information (such as a timestamp) to the transmission module before each round of transmission so that the receiver can align correctly.

[0092] (2) Bob Protocol Logic Module. This module implements all protocol actions of the receiver and includes the following sub-modules: a) Inner product calculation module: This submodule receives the masquerading state from the transmission module. First, obtain the inverse unitary transform U† from the unitary operator definition module, and then calculate the restored state. Then, the fermion commutation operator Sf and the reference state are obtained from the commutation operator definition module. Calculate the intermediate state = Finally, calculate the inner product. The inner product is a complex number, which ideally equals (-1)(k+1). This module outputs the calculated m to the k value determination module.

[0093] b) k-value determination module: This submodule receives the complex number m output by the inner product calculation module and maps it to the decoded bit k′ according to a preset decision rule. Specifically, if the real part of m is determined to be 1, then k′=1 is output; if the real part of m is determined to be -1, then k′=0 is output; otherwise, the transmission round is considered untrustworthy, and an invalid flag is output. The output of this module is the source of the key bits ultimately generated by the protocol.

[0094] c) State Storage Module: This submodule is responsible for temporarily storing the valid decoded bit k′ (or invalid flag) output by the k-value judgment module along with the corresponding round number in local memory. Simultaneously, it also receives the k value for the same round from the Alice end (via the classic channel) for calculating the bit error rate. This module maintains a record for each round: {round number, local k′, peer k (obtained from the classic channel), valid}.

[0095] (3) Transmission module (common) This module is responsible for transmitting camouflage states between Alice and Bob. The module represents the data. In a classical simulation environment, it serializes a four-dimensional complex vector into a byte stream, sends it to the peer via a high-speed interconnect network, and then deserializes it. In a real quantum hardware environment, the module controls a quantum state transmitter to generate physical quantum states, which are then transmitted through a quantum channel. The transmission module is also responsible for collecting channel state information, such as transmission delay, bit error rate estimates, and photon loss rate, and periodically reporting this information to the protocol state machine to determine whether the channel quality meets the requirements.

[0096] (4) Protocol state machine module This module maintains the state transitions of the entire key distribution session, ensuring that each step of the protocol is executed in the correct order and triggering corresponding error handling procedures in case of abnormal situations. The state machine defines states including: idle, initialization, parameter negotiation, encoded transmission, decoded measurement, public comparison, error correction, privacy amplification, completion, and abort. The state machine drives state transitions based on events such as start commands from the user interface module, round completion signals from the Alice and Bob protocol logic modules, and channel state feedback from the transmission module. Specifically, this module is responsible for controlling the n-round loop: from round 1 to round n, each round sequentially triggers Alice's encoded transmission and Bob's received measurement, and records the round counter.

[0097] IV. Quantum Simulation Layer The quantum simulation layer is the core supporting layer for this application to run on a classical computer. It is responsible for simulating the evolution, transformation, and measurement of quantum states using linear algebra operations. This layer abstracts quantum states as complex vectors, unitary operators as complex matrices, and implements operations such as matrix-vector multiplication and inner product. This layer contains the following three modules: (1) State Vector Repository. This module provides functions for creating, reading, updating, and deleting four-dimensional complex vectors (representing the initial reference state). The state vector repository internally maintains a memory pool to store various quantum states generated during protocol operation, including: fixed reference states. The transmitted state generated by encoding Disguised Receive the recovered intermediate state after applying Sf Each state vector has a unique identifier and reference count, and deep copying is supported to ensure that multiple operation modules do not interfere with each other.

[0098] (2) Unitary Operator Pool. This module pre-stores various unitary operators that may be used during protocol execution, mainly including: random unitary operators U and their inverses U† loaded from the key management layer, and fixed fermion commutation operators Sf. The unitary operator pool stores these operators in matrix form (4×4 complex array) and provides an interface for multiplication of operators with state vectors.

[0099] (3) Measurement Calculator. This module implements the measurement operations in the protocol, mainly inner product measurement. Specifically, the measurement calculator accepts two state vectors (both four-dimensional complex vectors) as input and calculates their dot product: This returns a complex number result. In an ideal simulation, this calculation is a precise floating-point operation. The output of this module is directly used by the k-value determination module in the Bob protocol logic.

[0100] V. Hardware Layer The hardware layer provides the physical computing resources and basic operating environment for the entire system. This system can be deployed on a high-performance computing cluster or a single server. The hardware layer includes the following four components: (1) CPU Cluster. Composed of multiple multi-core central processing units, responsible for executing the computational tasks of all upper-layer software modules. Specifically, this includes: matrix multiplication (for unitary transformation), vector dot product (for inner product measurement), random number generation algorithm, protocol state scheduling logic, network communication protocol stack, and user interface rendering. For large-scale key generation (e.g., n>106), the CPU cluster can utilize multi-threaded parallel processing and finally summarize the results.

[0101] (2) Storage System. This includes large-capacity memory and high-speed non-volatile storage. Memory is used to dynamically store state vectors, operator matrices, intermediate computation results, and protocol state variables. Memory should be large enough to accommodate multiple rounds of simulation data performed simultaneously. Solid-state drives are used for persistent storage of the original key, final security key, audit logs, and system configuration files. The storage system supports data encryption and integrity verification to prevent sensitive information from being read or tampered with without authorization.

[0102] (3) Job Management Unit. This component is responsible for scheduling and managing key distribution tasks. When the system provides key distribution services to multiple users or applications simultaneously, the job management unit allocates computing resources to each task based on priority and resource availability (number of idle CPU cores, memory availability, network bandwidth), and monitors the execution status of each task (running, completed, failed). The job management unit also supports task queuing, fault recovery, and load balancing. After the session ends, the job management unit collects the actual resource usage of each task for performance analysis and billing.

[0103] (4) High-speed interconnect network. This component connects the nodes within the CPU cluster to the servers of the communicating parties (Alice and Bob). The high-speed interconnect network uses 10 Gigabit Ethernet technology to provide low-latency, high-bandwidth data transmission capabilities. This network carries two types of data streams: one is the classical control information stream, including initialization parameter negotiation, public comparison, etc., which is transmitted after being encrypted through a secure transmission platform; the other is the data stream simulating quantum states, i.e., dummy states. The byte stream is a serialized version of a four-dimensional complex vector, which simulates a public quantum channel.

[0104] Furthermore, to enable those skilled in the art to better understand and implement this application, a detailed description is provided below with reference to a specific embodiment. For example... Figure 4The diagram shows another system implementation flowchart of this embodiment. This embodiment uses the secure distribution of binary keys as an application scenario to fully demonstrate the implementation process of this system. The software program of this system is deployed on one or more high-performance computing servers interconnected by a network. These servers are equipped with multi-core central processing units, large-capacity memory, and high-speed solid-state drives. The specific implementation steps are as follows: Step 1: Key Distribution System Initialization. The two communicating parties (Alice and Bob) establish a connection through an authenticated secure channel (Shenzhen Yongda Secure Transmission Platform). First, two-way authentication is performed to confirm the security of both parties' identities; then, they jointly determine the underlying quantum state representation system used for this session: In this embodiment, a two-particle spin system is used to simulate identical fermions, the Hilbert space is 4-dimensional, and the basis vectors are taken as the direct product basis. Both parties agreed on the initial quantum state. Subsequently, both parties negotiated and stored the 4×4 unitary operator U used in this session through the Shenzhen Yongda Secure Transmission Platform, and agreed on the explicit matrix form of the fermion commutation operator Sf.

[0105] Step Two: Data Encoding. The data encoding module on the Alice side begins its work. First, the pseudo-random number generator generates a random bit k∈{0,1}. Then, based on the value of k, the initial state is... Encoding is performed: the encoding rule is based on the value of k, which determines... The number of inversions, if k=0, then the sending state If k=1, then the sending state .

[0106] Step 3: The sending end's appearance is blurred. The encoded sending state... Before entering the public channel, a pre-negotiated unitary operator U is applied through the appearance transformation module to generate a camouflaged state. .because After transformation The first column. The disguised state presents as a random distribution with equal amplitude for each component under the standard basis, which cannot be directly interpreted by the eavesdropper.

[0107] Step 4: Data transmission. (In disguised state) The quantum state is transmitted to Bob's end via a public channel. During this process, any eavesdropper intercepting it will only receive a disguised quantum state. Since the eavesdropper does not know the specific form of U, even if... Even with a complete state tomography, only random complex amplitudes can be obtained; the original transmitting state cannot be deduced. still Therefore, it is impossible to obtain the key bit k.

[0108] Step 5: Receiving end appearance recovery. Bob receives the masquerading state. Then, it is immediately imported into the inverse transformation module. This module applies the inverse unitary transformation U† based on the U parameters synchronized with Alice during the initialization phase. In this embodiment, U is a real orthogonal matrix, U† = U The recovered state is calculated. In an ideal situation, .

[0109] Step Six: Measurement and Key Generation. Bob measures the recovered state to extract the key. The specific steps are as follows: (1) To Applying the fermion commutation operator Sf, we obtain .

[0110] (2) Calculation With local reference state inner product In classical simulations, this is achieved through a dot product.

[0111] (3) Make a decision based on the value of m: if m = +1, output k′ = 1; if m = -1, output k′ = 0; otherwise mark this round as invalid and request a retransmission.

[0112] (4) Record Alice's k and Bob's k′, and k = k′ under undisturbed conditions.

[0113] (5) Repeat steps two through six for a total of n rounds (e.g., n = 10) 5 ), to obtain the n-bit raw key.

[0114] As can be seen from the above specific implementation methods, this application utilizes the antisymmetry of identical particles for phase encoding and masquerades the transmission state through random unitary transformation, achieving secure and efficient quantum key distribution. This embodiment has a clear engineering implementation path. Based on the description of this embodiment, those skilled in the art can fully reproduce or modify this application without any inventive effort.

[0115] Furthermore, another alternative implementation method is proposed: implementation based on real quantum hardware. In the future, when both communicating parties possess programmable quantum computers or quantum communication devices (such as ion traps or superconducting qubit systems), this method can be run directly on quantum hardware in the following manner: (1) Initialization: Two qubits are allocated on the quantum processor and initialized to... state (e.g.) ).

[0116] (2) Encoding: If the key bit k=1, then apply a global phase gate to the two qubits to make the state change (Equivalent to applying an Sf operation, which can be achieved by combining a SWAP gate and a Z gate).

[0117] (3) Disguise: Based on the pre-shared unitary matrix U, it is decomposed into several single-bit gates and two-bit gates, and applied to two qubits to obtain a disguised state.

[0118] (4) Transmission: Send two qubits to Bob through a quantum channel (or quantum network).

[0119] (5) Recovery: After receiving the qubit, Bob applies the inverse gate sequence corresponding to U† to recover the original encoded state. ).

[0120] (6) Measurement and decision: Bob applies an Sf gate to two qubits and then measures their connection with the gate. The overlap is significant. Due to the noise and eavesdropping risks inherent in real quantum channels, additional steps are required: randomly selecting a subset of bits for public comparison to estimate the bit error rate; if the bit error rate is below a threshold, then privacy amplification is performed on the remaining bits to extract the final security key.

[0121] In this implementation, the method becomes a complete quantum key distribution protocol that is resistant to eavesdropping. Compared with traditional protocols such as BB84, it has advantages such as simple phase encoding and no need to randomly select measurement bases.

[0122] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A quantum key distribution method based on the simulation of identical particle exchange symmetry, characterized in that, include: The two communicating parties establish a connection through an authenticated channel and negotiate to determine the initial reference state, unitary operator, and fermion commutation operator; The sender generates random bits. When the random bits have a first value, the initial reference state is used as the sending state. When the random bits have a second value, the fermion commutation operator is applied to the initial reference state once to obtain the sending state. The sender uses the unitary operator to perform a unitary transformation on the transmitted state to obtain a masquerading state, and then transmits the masquerading state to the receiver through a public channel. The receiver uses the inverse transform of the unitary operator to recover the received dummy state, thus obtaining the recovered state; The receiver applies the fermion exchange operator to the recovered state, calculates the inner product of the applied state and the initial reference state, and decodes the key bit corresponding to the random bit based on the value of the inner product to complete the distribution of the quantum key in this round.

2. The quantum key distribution method based on the simulation of identical particle exchange symmetry according to claim 1, characterized in that, The initial reference state is a joint state of two particles with spin-up, represented by a complex vector in a direct product basis.

3. The quantum key distribution method based on the simulation of identical particle exchange symmetry according to claim 1, characterized in that, The unitary operator is a complex unitary matrix that acts on the Hilbert space where the initial reference state is located. Its inverse transformation is the conjugate transpose of the unitary operator. The two communicating parties synchronize the unitary operator through an authenticated channel, and different sessions use different unitary operators. The fermion exchange operator is a matrix operator obtained by taking the negative of the standard two-particle state exchange operator.

4. The quantum key distribution method based on the simulation of identical particle exchange symmetry according to claim 1, characterized in that, When the random bit is a first value, the transmitting state is equal to the initial reference state; when the random bit is a second value, the transmitting state is the state after applying the fermion commutation operator to the initial reference state; the transmitting state is the initial reference state or its negative vector.

5. The quantum key distribution method based on the simulation of identical particle exchange symmetry according to claim 1, characterized in that, The masquerading state is the product of the unitary operator and the transmitting state; the receiver applies the inverse transformation of the unitary operator to the masquerading state to obtain the recovering state.

6. The quantum key distribution method based on the simulation of identical particle exchange symmetry according to claim 1, characterized in that, The receiver applies the fermion commutation operator to the recovered state, and then the method further includes: Calculate the inner product of the initial reference state and the recovered state after applying the fermion exchange operator; when the inner product is of the first polarity, the decoded key bits are the first value; when the inner product is of the second polarity, the decoded key bits are the second value; when the inner product does not satisfy the first polarity or the second polarity, the receiver marks this round of transmission as invalid and requests a retransmission from the sender through the authenticated channel.

7. The quantum key distribution method based on the simulation of identical particle exchange symmetry according to claim 1, characterized in that, The method further includes: The two communicating parties negotiate and determine the number of session rounds, and repeatedly execute the process of the sender generating random bits and the receiver decoding key bits to obtain a multi-bit raw key; During the multi-round transmission process, after the sender completes the previous round of transmission in the masquerade state and receives the acknowledgment signal from the receiver, it starts the generation and encoding of the next round of random bits. Before each round of transmission, the current round number and synchronization information are attached to the masquerade state and transmitted together. The two communicating parties compare the random bits generated by the sender with the key bits decoded by the receiver in at least some rounds through an authenticated channel to calculate the bit error rate. If the bit error rate is lower than a preset threshold, privacy amplification is performed on the key bits in the remaining rounds to extract the final security key.

8. The quantum key distribution method based on the simulation of identical particle exchange symmetry according to claim 1, characterized in that, The method is simulated and executed on a classical computer using linear algebra operations, where quantum states are represented by complex vectors, the unitary transform, the inverse transform, and the fermion commutation operator are all represented by complex matrices, and the inner product is implemented through vector inner product operations.

9. The quantum key distribution method based on the simulation of identical particle exchange symmetry according to claim 1, characterized in that, The method is executed on quantum hardware: Two qubits are allocated on the quantum processor and initialized to the initial reference state. The unitary transform and the inverse transform are implemented by applying a quantum gate sequence to the two qubits. The dummy state is transmitted through a quantum channel. The inner product is obtained by measuring the overlap probability between the recovered state after applying the fermion commutation operator and the initial reference state.

10. A quantum key distribution system based on the simulation of identical particle exchange symmetry, used to perform the method according to any one of claims 1-9, characterized in that, include: The initialization module is used by the two communicating parties to establish a connection through an authenticated channel and negotiate and determine the initial reference state, unitary operator, and fermion commutation operator. The encoding module is used by the sender to generate random bits. When the random bits are of a first value, the initial reference state is used as the transmission state. When the random bits are of a second value, the fermion commutation operator is applied to the initial reference state once to obtain the transmission state. The camouflage and transmission module is used by the sender to perform a unitary transformation on the transmitted state using the unitary operator to obtain a camouflage state, and then transmits the camouflage state to the receiver through a public channel. The recovery module is used by the receiver to recover the received dummy state by using the inverse transformation of the unitary operator to obtain the recovered state; The decoding module is used by the receiver to apply the fermion exchange operator to the recovered state, calculate the inner product of the applied state and the initial reference state, and decode the key bit corresponding to the random bit according to the value of the inner product, so as to complete the distribution of the quantum key in this round.

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