Controlled bidirectional remote transmission method for any quantum state

Abstract

The invention provides a controlled bidirectional remote transmission method of any quantum state, and relates to the technical field of quantum communication. According to the invention, a control party David and communication parties Alice, Bob and Candy are introduced to construct a cooperative communication system, and the three communication parties all have receiving and transmitting bidirectional functions, so that the limitation of traditional one-way transmission is broken. Two core communication paradigms of quantum invisible transmission and remote state preparation are creatively fused, a maximum entanglement state sharing mechanism is constructed between a communication party and a control party, and bidirectional interactive transmission of quantum information is realized under cooperative regulation and control of the control party: Alice can invisibly transmit any single-bit state and two-bit state to Bob and Candy respectively, and Alice can invisibly transmit any single-bit state and two-bit state to Bob and Candy respectively; at the same time, Bob and Candy can also be used for jointly and remotely preparing any two bit states for Alice. In a transmission process, a receiver can perfectly reconstruct a target quantum state through a series of quantum measurement and unitary transformation operations, so that deterministic bidirectional hybrid transmission of quantum information is achieved. According to the technical scheme, organic fusion of two quantum communication modes is achieved, a multi-node collaborative quantum information interaction architecture is constructed, a core technology foundation is laid for constructing an efficient and flexible quantum communication network, and the application potential of quantum information transmission is remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of quantum communication, in particular to a controlled bidirectional remote transmission method of arbitrary quantum states. BACKGROUND

[0002] Quantum entanglement is a valuable resource in quantum information science and is widely used. Among them, quantum teleportation (QT) and remote state preparation (RSP) are two important communication technologies. In 1993, Bennett et al. first proposed the concept of QT, which is used to safely transmit an unknown quantum state to a remote receiver. The sender holds the state but has no information about it. In 2000, Lo proposed the RSP method based on the QT idea, which can transmit a known quantum state to a remote receiver. Unlike QT, the sender can choose the appropriate measurement basis for quantum bit measurement based on the known state information to be transmitted. In recent years, QT and RSP have received widespread attention from scholars.

[0003] In the field of quantum communication, in addition to independent quantum teleportation (QT) and remote state preparation (RSP) protocols, hybrid protocols that combine the two have gradually become a research hotspot. Sang et al. first proposed an innovative bidirectional controlled quantum information transmission method, which combines the core ideas of QT and RSP. With the assistance of the controller Charlie, bidirectional quantum state transmission between the two parties is achieved: Alice can transmit an unknown single-bit quantum state to Bob, while Bob can remotely prepare a known single-bit quantum state for Alice. This bidirectional communication mechanism not only guarantees the secure transmission of information in both directions, but also significantly improves the flexibility and efficiency of quantum communication, laying the foundation for building complex quantum networks.

[0004] Since the bidirectional hybrid quantum communication method was proposed, the academic community has derived various bidirectional hybrid quantum communication methods. Most current methods focus on symmetric quantum information transmission, i.e., the number of quantum state bits exchanged between the two parties is completely equal. However, in actual communication networks, user demands often exhibit differentiation - for example, in some scenarios, one party needs to transmit multiple-bit quantum states, while the other party only needs to feedback a small amount of quantum information; or there are complex scenarios where multiple communication nodes need to simultaneously exchange information.

[0005] Therefore, the study of new communication methods for quantum information transmission in actual communication networks (where the number of quantum state bits transmitted by the two parties is not equal) and multi-to-multi quantum communication models (where multiple senders and multiple receivers simultaneously implement bidirectional information exchange) is a key direction to adapt to actual network needs. This type of research can break through the limitations of symmetric transmission, improve the adaptability of quantum communication networks to diverse scenarios, and has important theoretical and application value. SUMMARY

[0006] In view of the deficiencies in the prior art, the present application combines quantum teleportation and remote state preparation, and proposes a controlled bidirectional remote transmission method of arbitrary quantum states, involving asymmetric bidirectional information transmission in a many-to-many user scenario.In a communication network, a control party David, three communication parties Alice, Bob and Candy, who can act as both senders and receivers, are set up to form a four-party communication model.Under the help of the control party David, using a 13-bit maximum entangled state as a quantum channel, Alice wants to transmit an unknown single-bit quantum state to Bob and an unknown two-bit quantum state to Candy, while Bob and Candy are willing to remotely prepare a known two-bit quantum state for Alice, so that the asymmetric bidirectional transmission of quantum information among multiple parties can be realized, which lays a core technical foundation for building an efficient and flexible quantum communication network and significantly improves the application potential of quantum information transmission.

[0007] The technical scheme of the present application is implemented as follows:

[0008] A controlled bidirectional remote transmission method of arbitrary quantum states, comprising the following steps:

[0009] S100, a bidirectional information transmission model is constructed, three communication parties Alice, Bob and Candy act as both senders and receivers, and under the help of the control party David, Alice transmits an unknown single-bit state to Bob and an unknown two-bit state to Candy.At the same time, Bob and Candy jointly remotely prepare an arbitrary known two-bit state for Alice where |·> represents a right arrow, a j ,b j ,c j ,j=0,1,2,3 are complex coefficients, and satisfy the normalization condition |a0| 2 +|a1| 2 =1, |b0| 2 +|b1| 2 +|b2| 2 +|b3| 2 =1, |c0| 2 +|c1| 2 +|c2| 2 +|c3| 2 =1.

[0010] S200, pre-share quantum entangled states, 13-bit maximum entangled states are shared between the given communication parties Alice, Bob and Candy, and the control party David as a quantum channel for information transmission.

[0011] S300: Alice performs three joint Bell base measurements; meanwhile, Bob and Candy perform two-qubit projection measurements on their own qubits respectively.

[0012] S400: Controller David performs single-qubit measurement.

[0013] S500: According to the measurement results, Alice, Bob and Candy perform appropriate recovery unitary transformation operations on the qubits in their hands respectively, and then reconstruct the correct target quantum state.

[0014] In a preferred embodiment of the present application, the arbitrary two-qubit state in step S100 is Let where θ0, θ1, θ2, θ3∈[0, 2π), r0, r1, r2, r3 represent real numbers, and satisfy the normalization condition r0 2 + r1 2 + r2 2 + r3 2 = 1.

[0015] The maximum entangled state of 13 qubits shared in step S2 is

[0016]

[0017] where Ω represents a quantum channel, denotes tensor operation, (·) 12 denotes the state of qubits 1 and 2, (·) 34 denotes the state of qubits 3 and 4, (·) 56 denotes the state of qubits 5 and 6, (·) 789 denotes the state of qubits 7, 8 and 9, (·) 10,11,12 denotes the state of qubits 10, 11 and 12, (·) 13 denotes the state of qubit 13.

[0018] The bit allocation method of the maximum entangled state |Ω> of 13 qubits in step S200 is: bits 1, 3, 5, 9 and 12 are allocated to the communication party Alice, bits 2, 7 and 10 are allocated to Bob, bits 4, 6, 8 and 11 are allocated to Candy, and bit 13 is kept by the controller David himself.

[0019] Therefore, the entire quantum system can be expressed in the following form

[0020]

[0021] The step S300 measures the process, Alice performs three Bell base measurements on the bit pairs (A0, 1), (A1, 3), (A2, 5) in turn, and the measurement base selected for the i (i = 1, 2, 3)th Bell base measurement is The form is as follows

[0022]

[0023] Meanwhile, Bob performs two-bit projection measurement on the measurement base As follows

[0024]

[0025] Then, according to the measurement result of Bob, Candy selects a suitable two-bit measurement base to perform two-bit projection measurement on the bits 8, 11. If the measurement result of Bob is Then the measurement base selected by Candy is As follows

[0026]

[0027] Here, the operations 1-j, j+2, 3-j are all modulo 4 addition operations.

[0028] In the step S400, the measurement base selected by David when performing single-bit measurement on the bit 13 is {|γ>, γ ∈ {0, 1}}.

[0029] In the step S500, Alice, Bob and Candy perform recovery unitary transformation operations R A , R B , R C on the bits in their hands respectively, so that the target transmission quantum state can be obtained as follows: Wherein, X and Z are Pauli matrices, and X 0 = Z 0 = I, I is a unit matrix, and they can be expressed in the form of density operators as follows: I = |0><0| + |1><1|, X = |0><1| + |1><0|, Z = |0><0| - |1><1|.

[0030] Compared with the prior art, the present application has the beneficial effects that:

[0031] 1) Innovative fusion communication mode, efficient transmission: the present application ingeniously fuses QT and remote RSP two communication modes, and constructs a controlled bidirectional remote transmission model of quantum state among four parties. Through sharing a maximum entangled state, with the assistance of the control party, three communication parties can successfully construct correct target quantum state at the same time through a series of quantum measurement and unitary transformation operations, and then achieve bidirectional mixed transmission of different quantum states among multiple parties.

[0032] 2) Low resource demand, simple operation and easy implementation: the present application is compatible with QT and remote RSP two communication modes, and only 13-bit quantum entangled state is needed as an information transmission carrier to complete bidirectional remote transmission of quantum information, without consuming a large amount of entangled resources. Moreover, the present application is relatively simple to operate, without complex quantum operations, and only Bell basis measurement, single-bit measurement, two-bit projection measurement and basic Pauli operation are needed to complete the communication task. These simple operations are more conducive to actual physical implementation. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 The model architecture diagram of the controlled bidirectional remote transmission of any quantum state provided by the method of the present application;

[0034] Figure 2 The step flow chart of the controlled bidirectional remote transmission of any quantum state provided by the method of the present application. DETAILED DESCRIPTION

[0035] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the present application.

[0036] As shown in the figure, Figure 1 the embodiment of the present application provides a controlled bidirectional remote transmission method of any quantum state, and the specific implementation steps are as follows:

[0037] S100, a bidirectional information transmission model is constructed, three communication parties Alice, Bob and Candy play both the sender and the receiver, and Alice transmits an unknown single-bit state to Bob, transmits an unknown two-bit state to Candy. At the same time, Bob and Candy jointly remotely prepare any two-bit state for Alice. Among them, |·> represents the right arrow, a j ,b j ,cj j = 0, 1, 2, 3 are complex coefficients, and satisfy the normalization condition |a0|2+ |a1|2+ |a2|2+ |a3|2= 1. 2 2 2 2 2 2 2 2 2 2 = 1.

[0038] For the convenience of description, for any known two-bit quantum state |φ3> = c0|00> + c1|01> + c2|10> + c3|11>, let where θ0, θ1, θ2, θ3∈ [0, 2π), r0, r1, r2, r3 represent real numbers, and satisfy the normalization condition r0 2 2 2 2 = 1.

[0039] S200, pre-shared quantum entangled state, given the communication parties Alice, Bob and Candy, and the controller David share 13-bit maximum entangled state |Ω> as a quantum channel, which can be expressed in the following form:

[0040]

[0041] Where bits 1, 3, 5, 9, 12 are assigned to Alice, bits 2, 7, 10 are assigned to Bob, bits 4, 6, 8, 11 are assigned to Candy, and bit 13 is kept by the controller David himself.

[0042] Thus, the entire quantum system of the information transmission process can be expressed as:

[0043]

[0044] S300, Alice performs three joint Bell basis measurements. Alice performs three joint Bell basis measurements on bit pairs (A0, 1), (A1, 3), (A2, 5) in turn, and the i-th (i = 1, 2, 3) Bell basis measurement selects the measurement basis Its form is expressed as follows:

[0045]

[0046] If the results of Alice's three Bell measurements are ​​​​​​​​​​​​So Alice sends two bits classical information m1n1=10 to Bob, and sends four bits classical information m2n2=01, m3n3=11 to Candy.

[0047] Meanwhile, Bob and Candy perform two bits projection measurement on their bits respectively. Bob performs two bits projection measurement on bits 7, 10 with measurement basis The form is shown as follows:

[0048]

[0049] Then according to Bob's measurement result, Candy chooses appropriate two bits measurement basis to perform projection measurement on bits 8, 11.

[0050] If Bob's measurement result is Bob sends two bits classical information st=10 to Candy, so Candy chooses two bits measurement basis The form is shown as follows:

[0051]

[0052] If Candy's measurement result is So Candy sends two bits classical information kl=01 to Alice.

[0053] At this time, the state of quantum system can be expressed as the form as follows:

[0054]

[0055] S400, the controller David performs single bit measurement. David performs single bit measurement on his bit 13 in single bit measurement basis {|γ>, γ∈{0, 1}}. If David gets the measurement result as |0>, so he publishes his measurement result in the form of classical information γ=0 on the public broadcast channel.

[0056] At this time, the state of quantum system becomes

[0057]

[0058] S500, according to the measurement result, Alice, Bob and Candy perform appropriate recovery unitary transformation operation R A , R B , R C on the quantum bits in their hands respectively, and further reconstruct the correct target quantum state. Wherein, R A represents the recovery unitary transformation operation performed by Alice, R B represents the recovery unitary transformation operation performed by Bob, RC represents the recovery unitary operation performed by Candy, where X and Z are Pauli matrices, and X 0 = Z 0 = I, which can be expressed in density operator form as I = |0><0| + |1><1|, X = |0><1| + |1><0|, Z = |0><0| - |1><1|.

[0059] According to the received classical information, Alice performs a unitary operation on the quantum bits 9 and 12 in her hand in the following form

[0060]

[0061] Meanwhile, Bob performs a unitary operation on the quantum bit 2 in his hand in the following form

[0062] R B = X2.

[0063] Candy performs a unitary operation on the quantum bits 4 and 6 in her hand in the following form

[0064]

[0065] Thus, Alice, Bob and Candy can respectively reconstruct the correct target quantum state

[0066] After the above series of measurement operations and recovery unitary transformation operations, the receiving party can successfully construct the correct target quantum state, thereby realizing asymmetric bidirectional transmission of quantum information. The controlled bidirectional remote transmission method of arbitrary quantum states described in the present application has a total of 4 × (4 × 4) × (4 × 16) × 2 = 2 13 measurement results, since there are many measurement results, they will not be described one by one. The relationship between Alice's part of the measurement results and the corresponding unitary operation is shown in Table 1, and the relationship between Bob's and Candy's part of the measurement results and the corresponding unitary operation is shown in Table 2.

[0067] Table 1 Relationship between Alice's part of the measurement results and Bob's and Candy's recovery unitary operation

[0068]

[0069]

[0070] Table 2 Relationship between Bob's and Candy's part of the measurement results and Alice's recovery unitary operation

[0071]

[0072]

[0073] The above description is only the preferred embodiment of the present application, and is not used to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for controlled bidirectional remote transfer of arbitrary quantum states, characterized by: A four-party collaborative system is constructed by introducing a control party David and three communication parties Alice, Bob and Candy, so that the three communication parties have both sending and receiving functions to break through the limitation of traditional one-way transmission. Meanwhile, the system innovatively integrates two core communication paradigms of quantum teleportation and remote state preparation to form a new transmission mechanism, and realizes two-way interaction of quantum information under the collaborative regulation of the control party: Alice wants to transmit arbitrary single-bit and two-bit states to Bob and Candy, while Bob and Candy jointly remotely prepare arbitrary two-bit states for Alice. During the information transmission process, the receiver can perfectly reconstruct the target state through quantum measurement and unitary transformation operation, achieving deterministic two-way mixed transmission of quantum information and providing core technical support for efficient and flexible quantum communication network. The steps are as follows: S100、Constructing a two-way information transmission model, three communication parties Alice, Bob and Candy both play the role of sender and receiver, with the help of the controller David, Alice transmits an unknown single-bit state to Bob, transmits an unknown two-bit state to Candy. At the same time, Bob and Candy jointly remotely prepare an arbitrary two-bit state for Alice where, represents an unknown arbitrary single-bit state, represents an unknown arbitrary two-bit state, represents a known arbitrary two-bit state, |·> represents the right arrow, a j ,b j ,c j , j = 0, 1, 2, 3 are complex coefficients, and satisfy the normalization condition |a0| 2 + |a1| 2 = 1, |b0| 2 + |b1| 2 + |b2| 2 + |b3| 2 = 1, |c0| 2 + |c1| 2 + |c2| 2 + |c3| 2 = 1; S200, pre-shared quantum entangled state, given the communication parties Alice, Bob and Candy, and the control party David share 13 bits of maximum entangled state as quantum channel for information transmission; S300, Alice performs three joint Bell basis measurements; at the same time, Bob and Candy perform two-bit projection measurements on their own bits respectively; S400, the control party David performs single-bit measurement; S500, according to the measurement results, Alice, Bob and Candy perform appropriate recovery unitary transformation operation on the quantum bits in their hands, and then reconstruct the correct target quantum state.

2. The method for controlled bidirectional remote transfer of arbitrary quantum states as claimed in claim 1, wherein, The 13-bit maximum entangled state shared in step S200 is where Ω denotes the quantum channel, denotes the tensor operation, (·) 12 denotes the state of qubits 1, 2, (·) 34 denotes the state of qubits 3, 4, (·) 56 denotes the state of qubits 5, 6, (·) 789 denotes the state of qubits 7, 8, 9, (·) 10,11,12 denotes the state of qubits 10, 11, 12, |·> 13 denotes the state of qubit 13.

3. The method for controlled bidirectional remote transfer of arbitrary quantum states as claimed in claim 2, wherein, The bit allocation method of the 13-bit entangled state in step S200 is: bits 1, 3, 5, 9 and 12 are allocated to the communication party Alice, bits 2, 7 and 10 are allocated to Bob, bits 4, 6 and 8 are allocated to Candy, and bit 13 is kept by the controller David himself.

4. The method for controlled bidirectional remote transfer of arbitrary quantum states as claimed in claim 3, wherein, Any known two-bit state in the step S100 is Let where θ0, θ1, θ2, θ3∈[0, 2π), r0, r1, r2, r3 represent real numbers, and satisfy the normalization condition r0 2 + r1 2 + r2 2 + r3 2 = 1.

5. The method for controlled bidirectional remote transfer of arbitrary quantum states as claimed in claim 4, wherein, The whole quantum system of the information transmission process in step S200 can be represented as follows:

6. The method for controlled bidirectional remote transfer of arbitrary quantum states as claimed in claim 5, wherein, In the step S300, Alice performs three Bell basis measurements on the bit pairs (A0, 1), (A1, 3), (A2, 5) in turn, and the measurement basis selected for the i-th (i = 1, 2, 3) Bell basis measurement is The form is expressed as follows:

7. The method for controlled bidirectional remote transfer of arbitrary quantum states as claimed in claim 6, wherein, In the step S300, the measurement bases of the two-bit projection measurement performed by Bob on bits 7 and 10 are The form is expressed as follows: Candy then chooses a suitable two-bit measurement basis to perform a two-bit projection measurement on bits 8 and 11 according to Bob's measurement result. If Bob's measurement result is then the measurement basis chosen by Candy is which can be expressed in the form Here, the operations 1-j, j+2, 3-j are all modulo 4 addition operations.

8. The method for controlled bidirectional remote transfer of arbitrary quantum states as claimed in claim 7, wherein, The measurement basis selected by David for single-bit measurement on bit 13 in step S400 is {|γ>, γ∈{0,1}}.

9. The method for controlled bidirectional remote transfer of arbitrary quantum states as claimed in claim 8, wherein, In the step S500, Alice, Bob and Candy respectively perform a recovery unitary transformation operation R on the bits remaining in their hands A , R B , R C , so that the target transmission quantum state can be obtained as: where X and Z are Pauli matrices, and X 0 = Z 0 = I, I is a unit matrix, which can be expressed in the form of a density operator as I = |0><0| + |1><1|, X = |0><1| + |1><0|, Z = |0><0| - |1><1|.

Images