Asymmetric controlled bidirectional mixed quantum communication method

Abstract

The invention provides an asymmetric controlled bidirectional mixed quantum communication method, which is used for solving the technical problem of limited communication requirements. In a communication network, a control party Frank and two communication parties Alice and Bob are arranged, and the Alice and the Bob can be used as a sending party and also can be used as a receiving party. Two communication modes are prepared in combination with quantum teleportation and remote state, the two communication parties and the control party share the maximum entanglement state, under the help of the control party, the two communication parties can send two quantum states with different bit numbers to the opposite party at the same time, and through a series of quantum measurement and unitary transformation operations, the unitary state of the two communication parties is obtained. A correct target quantum state can be successfully constructed, so that asymmetric perfect bidirectional hybrid transmission of the quantum state is realized. The two communication technologies of quantum invisible state transmission and remote state preparation are combined, two-way mixed transmission of quantum information between communication parties can be achieved, and the flexibility and efficiency of information transmission are greatly improved.

Description

Technical Field

[0001] The present invention relates to the field of quantum communication technology. By combining quantum teleportation and remote state preparation technology, asymmetric bidirectional transmission of quantum states between two communicating parties can be achieved, and in particular, refers to an asymmetric bidirectional hybrid quantum communication method. Background Art

[0002] Quantum entanglement, as an extraordinary resource in the field of quantum information science, has a wide range of applications that are remarkable. In this frontier exploration, two communication technologies, quantum teleportation and remote state preparation, are particularly prominent. In 1993, Bennett et al. first proposed the concept of quantum teleportation (QT) to securely transmit an unknown quantum state from a sender to another distant receiver. In quantum teleportation, the sender has the transmitted quantum state but knows nothing about the information of the state. In 2000, Lo first proposed the remote state preparation (RSP) method based on the idea of ​​quantum teleportation, which can transmit a known quantum state to a receiver far away in space. Unlike quantum teleportation, since the sender knows the information of the state to be transmitted, it can then choose a suitable measurement basis to measure the quantum bit. In recent years, researchers have conducted extensive research on various QT and RSP protocols.

[0003] In addition to the single QT and RSP communication protocols, communication protocols combining QT and RSP ideas have also been reported. In 2017, Sang designed a novel bidirectional controlled quantum information transmission scheme based on the QT and RSP ideas. With the help of the controller Charlie, Alice can transmit an unknown arbitrary single-bit quantum state to Bob, and Bob can remotely prepare a known arbitrary single-bit quantum state for Alice, realizing bidirectional transmission of quantum states. Bidirectional quantum communication allows information to be transmitted bidirectionally and securely between the two communicating parties, thereby increasing the flexibility and efficiency of communication.

[0004] Based on Sang's ideas, many scholars have proposed various two-way hybrid quantum communication schemes. Most of the two-way hybrid quantum communication schemes realize symmetric information transmission, and the two communicating parties can send quantum states with the same number of bits to each other. However, in actual communication networks, in order to meet the different communication needs of communication users in the communication network, it is very necessary to study new two-way hybrid quantum communication schemes. Summary of the invention

[0005] In view of the problem of limited communication demand in the above-mentioned background technology, the present invention combines quantum teleportation and remote state preparation as two communication methods, and proposes an asymmetric controlled bidirectional hybrid quantum communication method. In the communication network, a controller Frank and two communication parties Alice and Bob are set, where Alice and Bob can serve as both senders and receivers. With the help of the controller Frank, based on the seven-bit maximum entangled state as a quantum channel, Alice wants to transmit an unknown single-bit quantum state to Bob. At the same time, Bob is willing to remotely prepare a known two-bit quantum state for Alice, thereby realizing asymmetric bidirectional transmission of quantum information.

[0006] In order to achieve the above object, the technical solution of the present invention is achieved as follows:

[0007] An asymmetric controlled bidirectional hybrid quantum communication method is provided. A hybrid quantum communication model based on quantum teleportation and remote state preparation is constructed. Two communication parties and a control party share a seven-bit maximum entangled state in advance. One communication party is used as a sender and the other communication party is used as a receiver. By performing a series of quantum measurement and recovery unitary transformation operations, the receiver can successfully reconstruct target quantum states with different numbers of bits, thereby realizing asymmetric transmission of quantum information. The method includes the following steps:

[0008] Step S1: Construct a two-way communication model. The two communicating parties Alice and Bob act as both senders and receivers. With the help of the controller Frank, Alice wants to teleport an unknown single-bit quantum state to Bob. At the same time, Bob is willing to remotely prepare a known two-bit quantum state y>=x|00>+y|01>+z|10>+w|11> for Alice; where, represents the unknown single-bit quantum state to be transmitted, |·> represents the right vector, f represents the real coefficient, g represents the complex coefficient, and satisfies the normalization condition |f| 2 +|g| 2 =1; y represents the known two-bit quantum state to be transmitted, x represents the real coefficient, y, z, w represent the complex coefficients, and satisfy the normalization condition |x| 2 +|y| 2 +|z| 2 +|w| 2 =1;

[0009] Step S2: pre-share quantum entangled state, given that the communication parties Alice and Bob, and the control party Frank share a seven-bit maximum entangled state as a quantum channel for information transmission;

[0010] Step S3: Bob introduces two auxiliary particles to perform CNOT gate operation for channel modulation;

[0011] Step S4: Alice performs a joint Bell basis measurement; at the same time, Bob performs a four-bit projection measurement;

[0012] Step S5: the controller Frank performs single-bit measurement to obtain a measurement result;

[0013] Step S6: Based on the measurement results, Alice and Bob respectively perform a restoring unitary transformation operation on their respective quantum bits to reconstruct the correct target quantum state.

[0014] Preferably, the seven-bit maximum entangled state shared in step S2 is:

[0015]

[0016] Where Θ represents the quantum channel, represents tensor operations, (·) 12 represents the state of quantum bits 1 and 2, (·) 34 represents the state of quantum bits 3 and 4, (·) 56 represents the state of quantum bits 5 and 6, and |·>7 represents the state of quantum bit 7.

[0017] Preferably, the distribution method of the seven-bit entangled state |Θ> in step S2 is: particles (1, 4, 6) are distributed to the communication party Alice, particles (2, 3, 5) are distributed to the communication party Bob, and particle 7 is saved by the controller Frank himself.

[0018] Preferably, in step S3, Bob introduces two auxiliary particles |0> 3' and|0> 5' The quantum channel after performing the CNOT gate operation is:

[0019]

[0020] in,(·) 33'4 represents the states of quantum bits 3, 3', and 4, (·) 55'6 Indicates the states of quantum bits 5, 5', and 6; particles 3 and 5 are used as control bits, and 3' and 5' are used as corresponding target bits;

[0021] Therefore, the entire quantum system is expressed as:

[0022]

[0023] The asymmetric controlled bidirectional hybrid quantum communication method according to claim 4 is characterized in that, preferably, in step S3, the CNOT gate operation adopts the form of a density operator, expressed as CNOT=|00><00|+|01><01|+|10><11|+|11><10|; wherein <·| represents a left vector.

[0024] Preferably, the joint Bell measurement basis in step S4 is {|φ kl >,k,l∈{0,1}}, which is specifically expressed as follows:

[0025]

[0026] Preferably, the measurement basis used in the four-bit projection measurement in step S4 is {|ω mnst >,m,n,s,t∈{0,1}}, its specific form is as follows:

[0027]

[0028] Among them, matrices P and Q are both unitary matrices, and their expressions are:

[0029]

[0030] Among them, p 1 ·p 2 =x,p 1 ·q 2 =y,p 2 ·q 1 =z,q 1 ·q 2 =w;p 1 represents a real number, q 1 Indicates complex number, q 1* Represents the complex number q 1 The conjugate of 2 represents a real number, q 2 Indicates complex number, q 2* Represents the complex number q 2 conjugate of , and they also satisfy the condition |p 1 | 2 +|q 1 | 2 =1,|p 2 | 2 +|q 2 | 2 =1.

[0031] Preferably, the single-bit measurement basis in step S5 is {|r>, r∈{0,1}}.

[0032] Preferably, in step S6, Alice and Bob respectively perform a recovery unitary operation on their respective qubits, which is expressed as R B =(X k Z l⊕r )2; where R A represents the recovery unitary transformation operation performed by Alice, R B represents the recovery unitary transformation operation performed by Bob, X and Z are Pauli matrices, and X 0 =Z 0 =I, and are expressed in the form of density operators: I = |0><0|+|1><1|, X = |0><1|+|1><0|, Z = |0><0|-|1><1|.

[0033] Beneficial effects of the present invention:

[0034] 1) The present invention combines quantum teleportation and remote state preparation to prepare two communication modes. By sharing the maximum entangled state between two communicating parties and a controlling party, with the help of the controlling party, the two communicating parties can simultaneously send two quantum states with different numbers of bits to each other. After a series of quantum measurements and unitary transformation operations, the correct target quantum state can be successfully constructed, thereby realizing asymmetric perfect bidirectional hybrid transmission of quantum states.

[0035] 2) The present invention supports two communication modes, namely quantum teleportation and remote state preparation. It only requires a seven-bit quantum entangled state as an information transmission carrier to realize asymmetric transmission of quantum information. It does not require a large amount of quantum entanglement resources. It does not require complex quantum operations. The operation of the present invention is relatively simple. It only needs to perform Bell basis measurement, single-particle measurement, four-particle projection measurement and basic Pauli operation to complete the communication task. These simple operations are more conducive to physical realization. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0037] Figure 1 is a flow chart of the method of the present invention;

[0038] Figure 2 It is a quantum channel construction circuit diagram provided by the present invention;

[0039] Figure 3 It is a schematic diagram of proving the communication method provided by the present invention. DETAILED DESCRIPTION

[0040] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0041] like Figure 1 As shown, the embodiment of the present invention provides an asymmetric controlled bidirectional hybrid quantum communication method, which combines quantum teleportation and remote state preparation technology to build a hybrid quantum communication model. The two communicating parties and the control party share the seven-bit maximum entangled state in advance, where one communicating party acts as a sender and the other as a receiver. By performing a series of quantum measurement and recovery unitary transformation operations, the receiver can successfully reconstruct the target quantum state with different bit numbers, realizing the asymmetric transmission of quantum information. The specific implementation steps are as follows:

[0042] Step S1: Construct a two-way communication model. The two communicating parties Alice and Bob act as both senders and receivers. With the help of the controller Frank, Alice wants to teleport an unknown single-bit quantum state to Bob. At the same time, Bob is willing to remotely prepare a known two-bit quantum state y>=x|00>+y>01>+z|10>+w>11> for Alice; where, represents the unknown single-bit quantum state to be transmitted, |·> represents the right vector, f represents the real coefficient, g represents the complex coefficient, and satisfies the normalization condition |f| 2 +|g| 2 =1; y represents the known two-bit quantum state to be transmitted, x represents the real coefficient, y, z, w represent the complex coefficients, and they also satisfy the normalization condition |x| 2 +|y| 2 +|z| 2 +|w| 2 =1.

[0043] Step S2: pre-share quantum entangled state. Assume that the communication parties Alice and Bob, and the control party Frank share the seven-bit maximum entangled state as a quantum channel for information transmission. The construction line of the quantum channel |Θ> is as follows: Figure 2 shown.

[0044] The shared seven-qubit maximum entangled state is:

[0045]

[0046] Where Θ represents the quantum channel, represents tensor operations, (·) 12 represents the states of quantum bits 1 and 2, (·) 34 represents the states of quantum bits 3 and 4, (·) 56 represents the state of quantum bits 5 and 6, and |·>7 represents the state of quantum bit 7.

[0047] Here, Alice owns particle (1, 4, 6), Bob owns particle (2, 3, 5), and Frank holds particle 7.

[0048] Step S3: Quantum channel modulation, Bob introduces two auxiliary particles |0> 3' and|0> 5' , and perform the corresponding CNOT gate operation C 3,3' and C 5,5' , where particles 3 and 5 are used as control bits, and 3' and 5' are used as corresponding target bits, so the quantum channel becomes

[0049]

[0050] in,(·) 33'4 represents the states of quantum bits 3, 3', and 4, (·) 55'6 Indicates the states of quantum bits 5, 5', and 6.

[0051] The present invention uses a CNOT gate operation for channel modulation. The CNOT gate is a two-bit quantum gate, which can be expressed in the form of a density operator as CNOT=|00><00|+|01><01|+|10><11|+|11><10|; wherein <·| represents a left vector.

[0052] Therefore, the entire quantum system can be expressed as:

[0053]

[0054] Step S4: Bell basis measurement (BSM) and four-bit projection measurement (FQM), Alice measures her particle (a,1) in the measurement basis {|φ 00 >,|φ 01 >,|φ 10 >,|φ 11 >}, and then tell Bob the measurement result in the form of a classical message (k, l). If Alice obtains the measurement result of |φ 10 >,(kl=10), then it will tell Bob the two-bit classical message (1,0).

[0055] The Bell measurement basis is {φ kl >,k,l∈{0,1}}, which is specifically expressed as follows:

[0056]

[0057] At the same time, Bob measures his particle (3,3',5,5') in the four-bit measurement basis {|ω 0000 >,|ω 0010 >,|ω 0001 >,|ω 0011 >,|ω 1000 >,|ω 1010 >,|ω 1001 >,|ω 1011 >,|ω 0100 >,|ω 0110 >,|ω 0101 >,|ω 0111 >,|ω 1100 >,|ω 1110 >,|ω 1101 >,|ω 1111 >}, Bob tells Alice the measurement result in the form of a classical message (m,n,s,t). If the measurement result obtained by Bob is |ω 1010 >,(mnst=1010), then he will tell Alice the four-bit classical message (1,0,1,0).

[0058] The measurement basis used in the four-bit projection measurement is {|ω mnst >,m,n,s,t∈{0,1}}, its specific form is as follows:

[0059]

[0060] Among them, matrices P and Q are both unitary matrices, and their expressions are:

[0061]

[0062] Among them, p 1 ·p 2 =x,p 1 ·q 2 =y,p 2 ·q 1 =z,q 1 ·q 2 =w;p 1 represents a real number, q 1 Indicates complex number, q 1* Represents the complex number q 1 The conjugate of 2 represents a real number, q 2Indicates complex number, q 2* Represents the complex number q 2 conjugate of , and they also satisfy the condition

[0063] p 1 | 2 +|q 1 | 2 =1,|p 2 | 2 +|q 2 | 2 =1.

[0064] Specifically, the state of the system after measurement becomes

[0065]

[0066] Step S5: Single-bit measurement (SQM), the controller Frank performs single-bit measurement on his particle 7 under the single-bit measurement basis {|r>, r∈{0,1}}. If the measurement result obtained by Frank is |0>, he publishes his measurement result information r=0 in the form of classical information on the public broadcast channel.

[0067] At this point, the state of the quantum system becomes

[0068]

[0069] Step S6: Based on the measurement result information, Alice and Bob respectively perform appropriate restoring unitary transformation operations on the quantum bits in their hands, and then reconstruct the correct target quantum state.

[0070] Alice and Bob each perform a unitary recovery operation on the remaining qubits in their hands, and the expression is R B =(X k Z l⊕r )2; where R A represents the recovery unitary transformation operation performed by Alice, R B represents the recovery unitary transformation operation performed by Bob, X and Z are Pauli matrices, and X 0 =Z 0 =I, they can be expressed in the form of density operator as I = |0><0|+|1><1|, X = |0><1|+|1><0|, Z = |0><0|-|1><1|.

[0071] Alice and Bob perform the following unitary operation on qubits 4 and 6 based on the classical information they received:

[0072]

[0073] At the same time, Bob performs the following unitary operation on qubit 2:

[0074] R B =X2.

[0075] Alice and Bob are thus able to reconstruct the correct target quantum state.

[0076] After the above series of measurement operations and recovery unitary transformation operations, the receiver can successfully construct the correct target quantum state, thereby realizing asymmetric perfect bidirectional transmission of quantum information. The schematic diagram of the method of the present invention is shown in Figure 3 There are 128 measurement results in the asymmetric bidirectional hybrid quantum communication method of the present invention. Since there are many measurement results, they will not be described one by one. The relationship between some measurement results and the corresponding recovery unitary operation is shown in Table 1.

[0077] Table 1 Relationship between some measurement results and recovery unitary operation

[0078]

[0079]

[0080]

[0081] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. An asymmetric controlled bidirectional hybrid quantum communication method, characterized in that: A hybrid quantum communication model based on quantum teleportation and remote state preparation is constructed. The two communicating parties and the control party share the seven-bit maximum entangled state in advance. One communicating party acts as the sender and the other as the receiver. By performing a series of quantum measurement and recovery unitary transformation operations, the receiver can successfully reconstruct the target quantum state with different numbers of bits, realizing the asymmetric transmission of quantum information, including the following steps: Step S1: Construct a two-way communication model. The two communicating parties Alice and Bob act as both senders and receivers. With the help of the controller Frank, Alice wants to teleport an unknown single-bit quantum state to Bob. At the same time, Bob is willing to remotely prepare a known two-bit quantum state |ψ>=x|00>+y|01>+z|10>+w|11> for Alice; represents the unknown single-bit quantum state to be transmitted, |·> represents the right vector, f represents the real coefficient, g represents the complex coefficient, and satisfies the normalization condition |f| 2 +|g| 2 =1; ψ represents the known two-bit quantum state to be transmitted, x represents the real coefficient, y, z, w represent the complex coefficients, and the normalization condition |x| is satisfied. 2 +|y| 2 +|z| 2 +|w| 2 =1; Step S2: pre-share quantum entangled state, given that the communication parties Alice and Bob, and the control party Frank share a seven-bit maximum entangled state as a quantum channel for information transmission; Step S3: Bob introduces two auxiliary particles to perform CNOT gate operation for channel modulation; Step S4: Alice performs a joint Bell basis measurement; at the same time, Bob performs a four-bit projection measurement; Step S5: the controller Frank performs single-bit measurement to obtain a measurement result; Step S6: Based on the measurement results, Alice and Bob respectively perform a restoring unitary transformation operation on their respective quantum bits to reconstruct the correct target quantum state.

2. The asymmetric controlled bidirectional hybrid quantum communication method according to claim 1, characterized in that: The seven-bit maximum entangled state shared in step S2 is: Where Θ represents the quantum channel, represents tensor operations, (·) 12 represents the state of quantum bits 1 and 2, (·) 34 represents the state of quantum bits 3 and 4, (·) 56 represents the state of quantum bits 5 and 6, and |·>7 represents the state of quantum bit 7.

3. The asymmetric controlled bidirectional hybrid quantum communication method according to claim 2, characterized in that: The distribution method of the seven-bit entangled state |Θ> in step S2 is: particles (1, 4, 6) are distributed to the communication party Alice, particles (2, 3, 5) are distributed to the communication party Bob, and particle 7 is saved by the controller Frank himself.

4. The asymmetric controlled bidirectional hybrid quantum communication method according to claim 2, characterized in that: In step S3, Bob introduces two auxiliary particles |0> 3' and|0> 5' The quantum channel after performing the CNOT gate operation is: in,(·) 33'4 represents the states of quantum bits 3, 3', and 4, (·) 55'6 Indicates the states of quantum bits 5, 5', and 6; particles 3 and 5 are used as control bits, and 3' and 5' are used as corresponding target bits; Therefore, the entire quantum system is expressed as:

5. The asymmetric controlled bidirectional hybrid quantum communication method according to claim 4, characterized in that: In step S3, the CNOT gate operation is performed in the form of a density operator, which is expressed as CNOT=|00><00|+|01><01|+|10><11|+|11><10|; wherein <·| represents a left vector.

6. The asymmetric controlled bidirectional hybrid quantum communication method according to claim 1, characterized in that: The joint Bell measurement basis in step S4 is {|φ kl >,k,l∈{0,1}}, which is specifically expressed as follows:

7. The asymmetric controlled bidirectional hybrid quantum communication method according to claim 6, characterized in that: The measurement basis used in the four-bit projection measurement in step S4 is {|ω mnst >,m,n,s,t∈{0,1}}, its specific form is as follows: Among them, matrices P and Q are both unitary matrices, and their expressions are: Among them, p 1 ·p 2 =x,p 1 ·q 2 =y,p 2 ·q 1 =z,q 1 ·q 2 =w;p 1 represents a real number, q 1 Indicates complex number, q 1* Represents the complex number q 1 The conjugate of 2 represents a real number, q 2 Indicates complex number, q 2* Represents the complex number q 2 conjugate of , and they also satisfy the condition |p 1 | 2 +|q 1 | 2 =1,|p 2 | 2 +|q 2 | 2 =1.

8. The asymmetric controlled bidirectional hybrid quantum communication method according to claim 7, characterized in that: The single-bit measurement basis in step S5 is {|r>, r∈{0,1}}.

9. The asymmetric controlled bidirectional hybrid quantum communication method according to claim 8, characterized in that: In step S6, Alice and Bob respectively perform a unitary recovery operation on their respective qubits, which is expressed as Among them, R A represents the recovery unitary transformation operation performed by Alice, R B represents the recovery unitary transformation operation performed by Bob, X and Z are Pauli matrices, and X 0 =Z 0 =I, and are expressed in the form of density operators: I = |0><0|+|1><1|, X = |0><1|+|1><0|, Z = |0><0|-|1><1|.

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