Maximum entangled state sharing method in amplitude-damped channels based on coherence compensation

Abstract

The present invention provides a method for sharing maximum entangled states in an amplitude-damped channel based on coherence compensation, which relates to the field of quantum communication. Specifically, the distributor Alice prepares a maximum entangled Bell state based on single-particle A and single-particle T, and sends single-particle T to the receiver Bob via an amplitude-damped channel; the receiver Bob performs a quantum controlled NOT gate operation on the prepared single-particle B and the received single-particle T, and then sends single-particle T to the distributor Alice via an amplitude-damped channel; the distributor Alice performs a joint unitary operation on single-particle A and single-particle T, and then performs a single-particle Z-basis measurement on single-particle T, thereby achieving maximum entangled Bell state sharing between two parties in the amplitude-damped channel. This method is also applicable to maximum entangled GHZ state sharing between multiple parties in an amplitude-damped channel. The present invention adopts a coherence compensation mechanism to effectively suppress amplitude damping noise, thereby improving the fidelity of quantum teleportation and multi-party quantum state sharing.

Description

Technical Field

[0001] The present invention relates to the field of quantum communication, and in particular to a maximum entangled state sharing method in an amplitude damping channel based on coherence compensation. Background Art

[0002] Amplitude-damped noise can cause entanglement decoherence in the distribution of maximally entangled states in quantum channels, reducing the coherence of entangled quantum systems. This effect causes the distribution of maximally entangled states to degenerate into entangled mixed states, thereby reducing the fidelity of quantum teleportation and multi-party quantum state sharing schemes, ultimately making it impossible to accurately transmit quantum information.

[0003] To maintain the coherence of quantum states, entanglement purification techniques are currently the primary approach. This technique purifies noise-contaminated entangled mixed states into entangled states with higher entanglement. However, obtaining high-fidelity entangled pure states often requires multiple purification operations, which consumes significant quantum entanglement resources. Another approach is to employ decoherence-free quantum systems. These systems require specific symmetries between the quantum system and the surrounding system, but can only resist collective dephasing and collective rotation noise in the quantum channel and cannot effectively resist the effects of amplitude damping noise.

[0004] In addition to the two aforementioned methods, decoherence countermeasures are widely used in academia to suppress the decoherence effects of channel noise on quantum states. Quantum weak measurement theory is a common solution to the decoherence effects of amplitude-damped channels on the distribution of maximally entangled quantum states. However, this approach has significant drawbacks: it cannot completely suppress decoherence (i.e., it cannot achieve sharing of maximally entangled states in amplitude-damped channels), and its efficiency plummets to zero under heavy damping. To improve performance under heavy damping, researchers have proposed a hybrid scheme combining quantum weak measurement, environmentally assisted measurement, and quantum feedforward control. While this scheme can mitigate the efficiency drop, it still cannot completely suppress decoherence. Another effective approach is quantum entanglement compensation. This approach involves cyclically transmitting a single particle of a maximally entangled Bell state in amplitude-damped noise, introducing an auxiliary qubit, and performing a quantum controlled-NOT gate (CNOT gate) and a single-particle Z-basis measurement operation. This approach successfully achieves sharing of GHZ entangled pure states in amplitude-damped channels.

[0005] Therefore, in view of the limitations of existing technologies, it is urgent to develop a new method that can reliably share the maximum entangled state of a two-level quantum system in an amplitude-damped channel, which can effectively resist the decoherence effect caused by amplitude-damped noise and ensure the reliability of quantum teleportation and multi-party quantum state sharing schemes. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for sharing maximum entangled states in an amplitude-damped channel based on coherence compensation, which can compensate for the coherence of a two-level quantum system and offset the attenuation effect caused by the noise of the amplitude-damped channel, thereby suppressing the decoherence effect of the amplitude-damped channel on the quantum system and solving the problem of decreased fidelity of quantum teleportation and multi-party quantum state sharing schemes in the amplitude-damped channel.

[0007] To achieve the above objectives, the present invention provides a method for sharing maximum entangled states in an amplitude-damped channel based on coherence compensation. The amplitude-damped channel includes a distributor Alice and at least one receiver Bob.

[0008] When there is only one receiver Bob, the sharing method of the maximum entangled Bell state between the distributor Alice and the receiver Bob in the amplitude damped channel is as follows:

[0009] Step S101: The distributor Alice prepares a two-particle maximally entangled Bell state based on the single particle A and the single particle T she owns, and sends the single particle T to the receiver Bob via the amplitude damping channel.

[0010] Step S102: After receiving the single particle T, the receiver Bob performs a CNOT gate operation on the single particle B he prepared and the received single particle T, and then sends the single particle T to the distributor Alice through the amplitude damping channel.

[0011] Step S103: After receiving the single particle T, the distributor Alice performs a joint unitary operation on the single particle A and the single particle T.

[0012] Step S104: the distributor Alice performs a single-particle Z-basis measurement operation on the single particle T.

[0013] When there are multiple receivers Bob, the distributor Alice and multiple receivers Bob1, Bob2, ..., Bob s-1 The sharing method of the maximum entangled GHZ state is as follows:

[0014] Step S201: The distributor Alice prepares a two-particle maximally entangled Bell state based on the single particle A and the single particle T she owns, and sends the single particle T to the receiver Bob1 via the amplitude damping channel.

[0015] Step S202: After receiving the single particle T, the receiver Bob1 performs a CNOT gate operation on the prepared single particle B1 and the received single particle T, and then sends the single particle T to the receiver Bob2 through the amplitude damping channel.

[0016] Step S203: Receiver Bob k, k=2,…,s-2After receiving the single particle T, the single particle T and the local auxiliary particle B k Perform CNOT gate operation and then send the single particle T to the next receiver Bob through the amplitude damping channel k+1 ;in, represents the total number of quantum systems participating in the sharing of the maximum entangled GHZ state, i.e., the distributor Alice and multiple receivers Bob1, Bob2, ..., Bob s-1 The sum of the number of ; It is used to identify multiple receivers Bob1, Bob2, ..., Bob s-1 The index variable of the sequence.

[0017] Step S204: The last receiver Bob s-1 After receiving the single particle T, the single particle T and the local auxiliary particle B s-1 Perform the CNOT gate operation and then send the single particle T to the distributor Alice through the amplitude damping channel.

[0018] Step S205: After receiving the single particle T, the distributor Alice performs a joint unitary operation on the single particle A and the single particle T.

[0019] Step S206: The distributor Alice performs a single-particle Z-basis measurement operation on the single particle T.

[0020] Preferably, the combined unitary operation in step S103 There are two situations:

[0021] Case 1: When the maximum entangled Bell state prepared by the distributor Alice is or When the joint unitary operation The expression is:

[0022] ;

[0023] in, represents the strength of the amplitude damping channel; 、 They represent single particle A and single particle T in a two-level quantum system respectively; Indicates right arrow; Indicates the left arrow; and Both represent maximally entangled Bell states.

[0024] Case 2: When the maximum entangled Bell state prepared by the distributor Alice is or When the joint unitary operation The expression is:

[0025] ;

[0026] in, and Both represent maximally entangled Bell states.

[0027] Preferably, in step S104, the distributor Alice performs a single-particle Z-basis measurement operation on the single particle T. The specific results of the two situations in step S103 are as follows:

[0028] Case 1: If the quantum measurement result obtained by the distributor Alice is , the probability is , indicating that the quantum system between single particle A and single particle B successfully achieves coherence compensation, and the distributor Alice and the receiver Bob share the maximum entangled Bell state or Otherwise, the coherence compensation fails, and the composite quantum system between the distributor Alice and the receiver Bob is an entangled mixed state.

[0029] Scenario 2: If the quantum measurement result obtained by the distributor Alice is , the probability is , indicating that the quantum system between single particle A and single particle B successfully achieves coherence compensation, and the distributor Alice and the receiver Bob share the maximum entangled Bell state or Otherwise, the coherence compensation fails, and the composite quantum system between the distributor Alice and the receiver Bob is an entangled mixed state.

[0030] Preferably, the combined unitary operation in step S205 There are two situations:

[0031] Case 1: When the maximum entangled Bell state prepared by the distributor Alice is or When the joint unitary operation The expression is:

[0032] .

[0033] Case 2: When the maximum entangled Bell state prepared by the distributor Alice is or When the joint unitary operation The expression is:

[0034] .

[0035] Preferably, in step S206, the distributor Alice performs a single-particle Z-basis measurement operation on the single particle T. The specific results of the two situations in step S205 are as follows:

[0036] Case 1: If the quantum measurement result obtained by the distributor Alice is , the probability is , indicating that the distributor Alice and the receivers Bob1, Bob2, ..., Bob s-1 Sharing the maximum entangled GHZ state of s particles or Otherwise, the coherence compensation fails, and the distributor Alice and the receivers Bob1, Bob2, ..., Bob s-1 The quantum system composed of two components is an entangled mixed state; Represents the sum variable.

[0037] Scenario 2: If the quantum measurement result obtained by the distributor Alice is , the probability is , indicating that the distributor Alice and the receivers Bob1, Bob2, ..., Bob s-1 Sharing the maximum entangled GHZ state of s particles or Otherwise, the coherence compensation fails, and the distributor Alice and the receivers Bob1, Bob2, ..., Bob s-1 The quantum system that is compounded between them is an entangled mixed state.

[0038] Preferably, single particle B, single particle B1, local auxiliary particle B k and local auxiliary particle B s-1 The initial states are all prepared in the calculation ground state , single particle T is the control qubit, single particle B, single particle B1, local auxiliary particle B k and local auxiliary particle B s-1 are all target qubits.

[0039] Therefore, the present invention adopts the above-mentioned maximum entangled state sharing method in an amplitude damping channel based on coherence compensation, and the beneficial technical effects are as follows:

[0040] (1) By transmitting a single particle in the maximally entangled Bell state between the distributor Alice and the receiver Bob, and performing a CNOT gate operation by the receiver during the transmission process, and finally performing a joint unitary operation and a single-particle Z-basis measurement related to the amplitude damping strength parameter D by the distributor, the quantum decoherence effect caused by the amplitude damping channel is successfully offset, and the coherence compensation of the joint quantum system of the sender and the receiver is realized, thereby achieving high-fidelity sharing of the maximally entangled Bell state in a two-level quantum system in the amplitude damping channel.

[0041] (2) We designed entanglement compensation matrices for four different Bell states, enabling the sharing of all four types of maximally entangled Bell states. This method has good scalability and can be extended to multi-party scenarios with three or more parties, providing a flexible solution for constructing maximally entangled GHZ state quantum channels in quantum networks of different scales. This feature lays an important foundation for achieving reliable and fidelity-preserving quantum state teleportation or multi-party sharing in amplitude-damped channels, significantly improving the reliability and practical value of quantum state transmission in noisy environments.

[0042] (3) For the application scenario of multi-party quantum networks, this paper specifically proposes an entanglement compensation operation suitable for GHZ states. By transmitting particles multiple times and having each party perform CNOT gate operations in turn, and finally having the distributor perform joint unitary operations and measurements related to the amplitude damping strength, the coherence compensation and maximum entangled state recovery of the multi-party joint quantum system are successfully achieved. This innovative method not only enables the efficient sharing of multi-party maximum entangled GHZ states, but also exhibits excellent scalability and versatility, providing an effective technical means to improve the fidelity and practicality of entanglement distribution and quantum information processing in multi-party quantum networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Flowchart of the method for sharing the maximally entangled Bell state between the distributor Alice and the receiver Bob in an amplitude-damped channel;

[0044] Figure 2 Flowchart of the method for sharing the maximally entangled GHZ state between the distributor Alice and multiple receivers in an amplitude-damped channel. DETAILED DESCRIPTION

[0045] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0046] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0047] Example 1

[0048] like Figure 1 As shown in Figure 2, when there is only one receiver Bob, the sharing method of the maximum entangled Bell state between the distributor Alice and the receiver Bob in the amplitude damped channel is as follows:

[0049] Step S101: The distributor Alice prepares a two-particle maximally entangled Bell state based on the single particles A and T she owns, and sends the single particle T to the receiver Bob via an amplitude damped channel, where AD represents the amplitude damped channel.

[0050] Specifically, in a two-level quantum system, the maximum entangled Bell state of two quantum bits is a set of four orthogonal states, and the specific expression is:

[0051] ;

[0052] in, represents the maximally entangled Bell state of two quantum bits; Represents parameters; Represents the value of the quantum bit; represents a natural constant, ; represents an imaginary unit; Represents modular operation; The basis vector representing the first qubit represents the basis vector of the second qubit; 、 They represent single particle A and single particle T in a two-level quantum system respectively.

[0053] After sorting, we get four maximum entangled Bell states, the specific expressions are as follows:

[0054] ;

[0055] ;

[0056] ;

[0057] .

[0058] In this embodiment, the distributor Alice prepares the two-particle maximum entangled Bell state The expression is:

[0059] .

[0060] Step S102: After receiving the single particle T, the receiver Bob performs a CNOT gate operation on the single particle B prepared by him and the received single particle T.

[0061] Among them, the initial state of single particle B is prepared in the calculation ground state .

[0062] Specifically, a CNOT gate in a two-level quantum system is a two-qubit logic gate whose operation is based on the association between a control qubit and a target qubit. In this CNOT gate, the first qubit is the control qubit, and the second qubit is the target qubit.

[0063] CNOT door operation The specific expression is:

[0064] ;

[0065] in, represents the identity matrix; represents the Pauli-X matrix; represents the tensor product; Indicates right arrow; Indicates the left arrow;

[0066] In this embodiment, single particle T and single particle B are the control qubit and target qubit, respectively.

[0067] Subsequently, the receiver Bob sends the single particle T to the distributor Alice through the amplitude-damped channel.

[0068] Step S103: After receiving the single particle T, the distributor Alice performs a joint unitary operation on the single particle A and the single particle T.

[0069] The maximum entangled Bell state prepared by the distributor Alice obtained in step S101 is , so the joint unitary operation The expression is:

[0070] ;

[0071] in, Indicates the strength of the amplitude damping channel.

[0072] Step S104: the distributor Alice performs a single-particle Z-basis measurement operation on the single particle T.

[0073] The quantum measurement result obtained by distributor Alice is , the probability is , indicating that the quantum system between single particle A and single particle B successfully achieves coherence compensation, and the distributor Alice and the receiver Bob share the maximum entangled Bell state Otherwise, the coherence compensation fails, and the composite quantum system between the distributor Alice and the receiver Bob is an entangled mixed state.

[0074] Example 2

[0075] like Figure 2 As shown in the figure, when there are multiple receivers Bob, the distributor Alice and multiple receivers Bob1, Bob2, ..., Bob s-1 The sharing method of the maximum entangled GHZ state is as follows:

[0076] Step S201: The distributor Alice prepares a two-particle maximally entangled Bell state based on the single particle A and the single particle T she owns, and sends the single particle T to the receiver Bob1 via the amplitude damping channel.

[0077] Specifically, in a two-level quantum system, the maximum entangled Bell state of two quantum bits is a set of four orthogonal states, and the specific expression is:

[0078] ;

[0079] in, represents the maximally entangled Bell state of two quantum bits; Represents parameters; Represents the value of the quantum bit; represents a natural constant, ; represents an imaginary unit; Represents modular operation; The basis vector representing the first qubit represents the basis vector of the second qubit; 、 They represent single particle A and single particle T in a two-level quantum system respectively.

[0080] After sorting, we get four maximum entangled Bell states, the specific expressions are as follows:

[0081] ;

[0082] ;

[0083] ;

[0084] .

[0085] Step S202: After receiving the single particle T, the receiver Bob1 performs a CNOT gate operation on the single particle B1 it prepared and the received single particle T.

[0086] Among them, the initial state of single particle B1 is prepared in the calculation ground state .

[0087] Specifically, a CNOT gate in a two-level quantum system is a two-qubit logic gate whose operation is based on the association between a control qubit and a target qubit. In this CNOT gate, the first qubit is the control qubit, and the second qubit is the target qubit.

[0088] CNOT door operation The specific expression is:

[0089] ;

[0090] in, represents the identity matrix; represents the Pauli-X matrix; represents the tensor product; Indicates right arrow; Indicates left arrow.

[0091] In this embodiment, single particle T and single particle B1 are the control qubit and target qubit, respectively.

[0092] Subsequently, receiver Bob1 sends the single particle T to receiver Bob2 through the amplitude-damped channel.

[0093] Step S203: Receiver Bob k , k=2,…,s-2After receiving the single particle T, introduce the local auxiliary particle B k , for single particle T and local auxiliary particle B k Perform a CNOT gate operation.

[0094] Among them, the local auxiliary particle B k The initial state is prepared from the calculation ground state Single particle T and local auxiliary particle B k are the control qubit and the target qubit, respectively. represents the total number of quantum systems participating in the sharing of the maximum entangled GHZ state, i.e., the distributor Alice and multiple receivers Bob1, Bob2, ..., Bob s-1 The sum of the number of ; It is used to identify multiple receivers Bob1, Bob2, ..., Bob s-1 The index variable of the sequence;

[0095] Then, the receiver Bob k Send the single particle T to the next receiver Bob through the amplitude damped channel k+1 .

[0096] Step S204: The last receiver Bob s-1 After receiving the single particle T, the single particle T and the local auxiliary particle B s-1 Perform a CNOT gate operation.

[0097] Among them, the local auxiliary particle B s-1 The initial state is prepared from the calculation ground state Single particle T and local auxiliary particle B s-1 are the control qubit and the target qubit, respectively.

[0098] Then, the receiver Bob s-1The single particle T is sent to the distributor Alice through the amplitude-damped channel.

[0099] Step S205: After receiving the single particle T, the distributor Alice performs a joint unitary operation on the single particles A and T. , specifically divided into the following two situations:

[0100] Case 1: When the maximum entangled Bell state prepared by the distributor Alice is or When the joint unitary operation The expression is:

[0101] ;

[0102] Case 2: When the maximum entangled Bell state prepared by the distributor Alice is or When the joint unitary operation The expression is:

[0103] .

[0104] Step S206: The distributor Alice performs a single-particle Z-basis measurement operation on the single particle T. The specific results of the two situations in step S205 are as follows:

[0105] Case 1: If the quantum measurement result obtained by the distributor Alice is , the probability is , indicating that the distributor Alice and the receivers Bob1, Bob2, ..., Bob s-1 Sharing the maximum entangled GHZ state of s particles or Otherwise, the coherence compensation fails, and the distributor Alice and the receivers Bob1, Bob2, ..., Bob s-1 The quantum system composed of two states is an entangled mixed state. Represents the sum variable.

[0106] Scenario 2: If the quantum measurement result obtained by the distributor Alice is , the probability is , indicating that the distributor Alice and the receivers Bob1, Bob2, ..., Bob s-1 Sharing the maximum entangled GHZ state of s particles or Otherwise, the coherence compensation fails, and the distributor Alice and the receivers Bob1, Bob2, ..., Bob s-1 The quantum system that is compounded between them is an entangled mixed state.

[0107] Example 3

[0108] When there are two receivers, the method for sharing the maximum entangled GHZ state between the distributor Alice and the two receivers Bob1 and Bob2 in the amplitude damped channel is as follows:

[0109] Step S201: The distributor Alice prepares the two-particle maximum entangled Bell state based on the single particle A and the single particle T she owns. And send the single particle T to the receiver Bob1 through the amplitude damping channel.

[0110] Specifically, in a two-level quantum system, the maximum entangled Bell state of two quantum bits is a set of four orthogonal states, and the specific expression is:

[0111] ;

[0112] in, represents the maximally entangled Bell state of two quantum bits; Represents parameters; Represents the value of the quantum bit; represents a natural constant, ; represents an imaginary unit; Represents modular operation; The basis vector representing the first qubit represents the basis vector of the second qubit; 、 They represent single particle A and single particle T in a two-level quantum system respectively.

[0113] After sorting, we get four maximum entangled Bell states, the specific expressions are as follows:

[0114] ;

[0115] ;

[0116] ;

[0117] .

[0118] In this embodiment, the distributor Alice prepares the two-particle maximum entangled Bell state The expression is:

[0119] .

[0120] Step S202: After receiving the single particle T, the receiver Bob1 performs a CNOT gate operation on the single particle B1 it prepared and the received single particle T.

[0121] Among them, the initial state of single particle B1 is prepared in the calculation ground state .

[0122] Specifically, a CNOT gate in a two-level quantum system is a two-qubit logic gate whose operation is based on the association between a control qubit and a target qubit. In this CNOT gate, the first qubit is the control qubit, and the second qubit is the target qubit.

[0123] CNOT door operation The specific expression is:

[0124] ;

[0125] in, represents the identity matrix; represents the Pauli-X matrix; represents the tensor product; Indicates right arrow; Indicates left arrow.

[0126] In this embodiment, single particle T and single particle B1 are the control qubit and target qubit, respectively.

[0127] Subsequently, receiver Bob1 sends the single particle T to receiver Bob2 through the amplitude-damped channel.

[0128] Step S203: After receiving the single particle T, the receiver Bob2 introduces the local auxiliary particle B2 and performs a CNOT gate operation on the single particle T and the local auxiliary particle B2.

[0129] Among them, the initial state of the local auxiliary particle B2 is prepared in the calculation ground state , the single particle T and the local auxiliary particle B2 are the control qubit and the target qubit, respectively.

[0130] Subsequently, the receiver Bob2 sends the single particle T to the distributor Alice through the amplitude-damped channel.

[0131] Step S204: After receiving the single particle T, the distributor Alice performs the same amplitude damping channel strength test on the single particles A and T. D Related joint unitary operations.

[0132] The maximum entangled Bell state prepared by the distributor Alice obtained in step S201 is , so the joint unitary operation The expression is:

[0133] ;

[0134] Step S205: The distributor Alice performs a single-particle Z-basis measurement operation on the single particle T.

[0135] If the quantum measurement result obtained by the distributor Alice is , the probability is , indicating that the distributor Alice and the receivers Bob1 and Bob2 share the maximum entangled GHZ state ; Otherwise, coherence compensation fails and the tripartite composite quantum system is an entangled mixed state.

[0136] Therefore, the present invention adopts the above-mentioned maximum entangled state sharing method in the amplitude damping channel based on coherence compensation, which can compensate the coherence of the two-level quantum system and offset the attenuation effect caused by the amplitude damping channel noise, thereby suppressing the decoherence effect of the amplitude damping channel on the quantum system and solving the problem of decreased fidelity of quantum teleportation and multi-party sharing schemes in the amplitude damping channel.

[0137] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for maximum entangled state sharing in an amplitude damped channel based on coherence compensation, characterized in that: The amplitude-damped channel includes a distributor Alice and at least one receiver Bob; When there is only one receiver Bob, the method for sharing the maximum entangled Bell state between the distributor Alice and the receiver Bob in the amplitude damped channel is as follows: Step S101: The distributor Alice prepares a two-particle maximally entangled Bell state based on the single particle A and the single particle T she owns, and sends the single particle T to the receiver Bob via the amplitude damping channel; Step S102: After receiving the single particle T, the receiver Bob performs a CNOT gate operation on the single particle B he prepared and the received single particle T, and then sends the single particle T to the distributor Alice through the amplitude damping channel; Step S103: After receiving the single particle T, the distributor Alice performs a joint unitary operation on the single particle A and the single particle T; Step S104: the distributor Alice performs a single-particle Z-basis measurement operation on the single particle T; When there are multiple receivers Bob, the distributor Alice and multiple receivers Bob1, Bob2, ..., Bob s-1 The sharing method of the maximum entangled GHZ state is as follows: Step S201: The distributor Alice prepares a two-particle maximally entangled Bell state based on the single particle A and the single particle T she owns, and sends the single particle T to the receiver Bob1 via the amplitude damping channel; Step S202: After receiving the single particle T, the receiver Bob1 performs a CNOT gate operation on the prepared single particle B1 and the received single particle T, and then sends the single particle T to the receiver Bob2 through the amplitude damping channel; Step S203: Receiver Bob k , k=2,…,s-2After receiving the single particle T, the single particle T and the local auxiliary particle B k Perform CNOT gate operation and then send the single particle T to the next receiver Bob through the amplitude damping channel k+1 ;in, represents the total number of quantum systems participating in the sharing of the maximum entangled GHZ state, ; It is used to identify multiple receivers Bob1, Bob2, ..., Bob s-1 The index variable of the sequence; Step S204: The last receiver Bob s-1 After receiving the single particle T, the single particle T and the local auxiliary particle B s-1 Perform CNOT gate operation and then send the single particle T to the distributor Alice through the amplitude damping channel; Step S205: After receiving the single particle T, the distributor Alice performs a joint unitary operation on the single particle A and the single particle T; Step S206: the distributor Alice performs a single-particle Z-basis measurement operation on the single particle T; In step S104, the distributor Alice performs a single-particle Z-basis measurement operation on the single particle T. The specific results for the two situations in step S103 are as follows: Case 1: If the quantum measurement result obtained by the distributor Alice is , the probability is , indicating that the quantum system between single particle A and single particle B successfully achieves coherence compensation, and the distributor Alice and the receiver Bob share the maximum entangled Bell state or Otherwise, the coherence compensation fails, and the composite quantum system between the distributor Alice and the receiver Bob is an entangled mixed state; Scenario 2: If the quantum measurement result obtained by the distributor Alice is , the probability is , indicating that the quantum system between single particle A and single particle B successfully achieves coherence compensation, and the distributor Alice and the receiver Bob share the maximum entangled Bell state or Otherwise, the coherence compensation fails, and the composite quantum system between the distributor Alice and the receiver Bob is an entangled mixed state; ； ； ； 。 2. The method for maximum entangled state sharing in an amplitude damped channel based on coherence compensation according to claim 1, characterized in that: The unitary operation in step S103 There are two situations: Case 1: When the maximum entangled Bell state prepared by the distributor Alice is or When the joint unitary operation The expression is: ； in, represents the strength of the amplitude damping channel; 、 They represent single particle A and single particle T in a two-level quantum system respectively; Indicates right arrow; Indicates the left arrow; and Both represent maximally entangled Bell states; Case 2: When the maximum entangled Bell state prepared by the distributor Alice is or When the joint unitary operation The expression is: ； in, and Both represent maximally entangled Bell states.

3. The method for maximum entangled state sharing in an amplitude damped channel based on coherence compensation according to claim 2, characterized in that: The unitary operation in step S205 There are two situations: Case 1: When the maximum entangled Bell state prepared by the distributor Alice is or When the joint unitary operation The expression is: ； Case 2: When the maximum entangled Bell state prepared by the distributor Alice is or When the joint unitary operation The expression is: 。 4. The method for maximum entangled state sharing in an amplitude damped channel based on coherence compensation according to claim 3, characterized in that: In step S206, the distributor Alice performs a single-particle Z-basis measurement operation on the single particle T, for the two situations in step S205, specifically situation 1 and situation 2; Case 1: If the quantum measurement result obtained by the distributor Alice is , the probability is ; Scenario 2: If the quantum measurement result obtained by the distributor Alice is , the probability is ; Scenario 1 shows that the distributor Alice and the receivers Bob1, Bob2, ..., Bob s-1 Sharing the maximum entangled GHZ state of s particles or ; Otherwise, the coherence compensation fails, and the distributor Alice and the receivers Bob1, Bob2, ..., Bob s-1 The quantum system composed of two components is an entangled mixed state; Represents the sum variable.

5. The method for maximum entangled state sharing in an amplitude damped channel based on coherence compensation according to claim 1, characterized in that: Single particle B, single particle B1, local auxiliary particle B k and local auxiliary particle B s-1 The initial states are all prepared in the calculation ground state , single particle T is the control qubit, single particle B, single particle B1, local auxiliary particle B k and local auxiliary particle B s-1 are all target qubits.

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