Teleportation method for teleporting an unknown five-particle entangled state based on a five-particle cluster state

Abstract

The present invention discloses a teleportation method for teleporting an unknown five-particle entangled state based on a five-particle cluster state, which relates to the field of quantum communication technology and includes: a communication sender and a communication receiver share a five-particle cluster state to establish a quantum entanglement channel; the communication sender transforms the unknown five-particle entangled state to be teleported into an unknown GHZ-like state through a CNOT gate; the communication sender performs a Bell state measurement and an H gate operation on the unknown GHZ-like state according to the five-particle cluster state, and then informs the communication receiver of its own measurement result; the communication receiver performs a unitary operation on the particles it owns according to the measurement result of the communication sender and the five-particle cluster state to reconstruct the GHZ-like state; the communication receiver introduces auxiliary particles and restores the unknown five-particle entangled state by performing a CNOT gate operation on the reconstructed GHZ-like state. The present invention has the characteristics of high communication efficiency.

Description

Technical Field

[0001] The present invention relates to the field of quantum technology, and in particular to an invisible transmission method based on transmitting an unknown five-particle entangled state through a five-particle cluster state. Background Art

[0002] With the rapid development of quantum technology, quantum communication has attracted much attention at home and abroad because it can use quantum states as information carriers to transmit information unconditionally and securely. Traditional communication encryption technologies rely on the complexity of mathematical algorithms, but as long as the computing power is strong enough, even the most complex confidentiality algorithms can be cracked. The security of quantum communication is based on the basic principles of quantum mechanics, which can ensure that information cannot be eavesdropped or cracked. Quantum communication has brought revolutionary development to information security and has great application value in national security and finance. Quantum communication can be divided into quantum key distribution, quantum teleportation, quantum dense coding, quantum secret sharing and other directions. Various quantum states such as Bell states, GHZ states, W states and cluster states are used as different quantum channels to meet various quantum communication scenarios.

[0003] The cluster state is a new quantum entangled state proposed by Briegel and Raussendorf in 2001. The cluster state can only show some special properties when the number of particles N>3. For example, the cluster state contains the entangled characteristics of the GHZ state and the W state, and has maximum connectivity and entanglement stubbornness. In addition, Dür and Briegel have proved that the cluster state is less susceptible to decoherence than the GHZ state. The cluster state has high security as a quantum channel because the eavesdropper must perform complex measurements to eavesdrop on information. Due to these advantages, various quantum teleportation schemes for cluster states have been proposed in recent years. Some of the quantum teleportation schemes that have been proposed to transmit the five-particle entangled state are complicated to operate, such as using the more difficult von-Neumann measurement (this is a relatively complicated process, and its application in experiments will greatly increase the difficulty of the experiment), or directly transmitting the five-particle entangled state, which will use more quantum resources and classical resources, so most of them have the defect of low transmission efficiency. Summary of the invention

[0004] The present invention provides a teleportation method based on transmitting an unknown five-particle entangled state through a five-particle cluster state, which can alleviate the above-mentioned problems.

[0005] In order to alleviate the above-mentioned problems, the technical solution adopted by the present invention is as follows:

[0006] The present invention provides a teleportation method based on transmitting an unknown five-particle entangled state via a five-particle cluster state, comprising:

[0007] The communication sender and the communication receiver share a five-particle cluster state |η>12345 , establish a quantum entanglement channel;

[0008] The communication sender transforms the unknown five-particle entangled state to be transmitted into an unknown GHZ-like state through the CNOT gate;

[0009] The communication sender uses the five-particle cluster state |η> 12345 , perform Bell state measurement and H-gate operation on the unknown GHZ-like state, and then inform the communication receiver of its own measurement results;

[0010] The communication receiver uses the measurement results of the communication sender and the five-particle cluster state |η〉 12345 , perform unitary operations on the particles you own and reconstruct the GHZ state;

[0011] The communication receiver introduces auxiliary particles and recovers the unknown five-particle entangled state by performing CNOT gate operations on the reconstructed GHZ-like state.

[0012] The prior art directly transmits the unknown five-particle entangled state. The present invention converts the unknown five-particle entangled state to be transmitted into a GHZ-like state through a CNOT gate, thereby reducing the consumption of quantum resources and classical resources during the transmission process.

[0013] The operation performed by the communication sender in the prior art is relatively complicated. The communication sender in the present invention performs the operation of performing ... 12345 , perform Bell state measurement and H-gate operation on unknown GHZ-like states, and then inform the communication receiver of your own measurement results through the classical channel, which is simpler to operate.

[0014] Compared with the prior art, the present invention consumes less quantum resources and classical resources, the operations of the communicating parties are simple and the steps are fewer, and more quantum resource transmission is achieved by using fewer channel quantum bits, thereby greatly improving the transmission efficiency.

[0015] In a preferred embodiment of the present invention, the five-particle cluster state

[0016]

[0017] Among them, the communication sender owns particles 2 and 5, while the communication receiver owns particles 1, 3, and 4.

[0018] In a preferred embodiment of the present invention, the communication sender performs two CNOT gate operations in the process of transforming the unknown five-particle entangled state to be transmitted into an unknown GHZ-like state.

[0019] In a preferred embodiment of the present invention, the CNOT gate is a 2-bit quantum bit gate. During the operation of the CNOT gate, when the control bit is 1, the target bit is inverted, otherwise the target bit remains unchanged.

[0020] In a preferred embodiment of the present invention, the Bell basis used in Bell state measurement is:

[0021]

[0022] In a preferred embodiment of the present invention, the H gate operation is:

[0023] In a preferred embodiment of the present invention, the communication sender informs the communication receiver of its measurement results through a classical channel.

[0024] In a preferred embodiment of the present invention, the unitary operations performed by the communication receiving party are four Pauli operators:

[0025] I=|0><0|+|1><1|,σ x =|0><1|+|1〉〈0|, -iσ y =|1><0|-|0><1|,σ z =|0><0|-|1><1|.

[0026] In a preferred embodiment of the present invention, the communication receiving party performs two CNOT gate operations on the reconstructed GHZ-like state.

[0027] In a preferred embodiment of the present invention, the communication receiver introduces two auxiliary particles: |00> fg .

[0028] Compared with the prior art, the beneficial effects of the present invention are: the method of the present invention completes the transmission of the unknown five-particle entangled state by sharing the five-particle cluster state entangled channel between the communicating parties. The whole process can perform Bell state measurement, classical communication and local operation. The five-particle cluster state as a quantum channel not only has low quantum resource consumption but also increases security and has the characteristics of high communication efficiency.

[0029] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the embodiments of the present invention are specifically cited below and described in detail with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0031] Figure 1It is a flow chart of a quantum teleportation scheme based on a five-particle cluster state to transmit an unknown five-particle entangled state provided by the present invention;

[0032] Figure 2 It is a schematic diagram of particle allocation of the sender Alice and the receiver Bob in the solution of the present invention;

[0033] Figure 3 It is a quantum circuit diagram of a quantum teleportation scheme for transmitting a five-particle entangled state based on a five-particle cluster state by a sender Alice and a receiver Bob in the scheme of the present invention. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings 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.

[0035] Example

[0036] The two communicating parties in this embodiment are Alice and Bob, Alice is the first communicating party, and Bob is the second communicating party. Alice wants to transmit an unknown five-particle entangled state |ξ> abcde To Bob, this unknown five-particle entangled state |ξ〉 abcde The form is as follows:

[0037] |ξ> abcde =(α|00000>+β|00111>+γ|11101〉+δ|11010〉) abcde

[0038] Among them, the four coefficients are unknown parameters, and they satisfy the normalization condition |α| 2 +|β| 2 +|γ 2 +|δ| 2 =1.

[0039] In order to achieve the transmission of quantum information, the sender Alice and the receiver Bob need to share a five-particle cluster state |η〉 12345 As a quantum channel, the form is as follows:

[0040]

[0041] Among them, the sender Alice has particles a, b, c, d, e, 2, 5, and the receiver Bob has particles 1, 3, 4. The particle allocation diagram of the sender Alice and the receiver Bob is as follows Figure 2 shown.

[0042] Please refer to Figure 1 , Figure 2 and Figure 3 The present invention is based on the five-particle cluster state |η〉 12345 Teleporting an unknown five-particle entangled state |ξ> abcde The quantum teleportation method includes the following steps:

[0043] Step 1: The sender Alice first uses particle b as the control bit and particle a as the target bit to perform a CNOT gate operation, and then uses particle c as the control bit and particle e as the target bit to perform a CNOT gate operation to transfer the unknown five-particle entangled state |ξ> abcde Transformed into an unknown GHZ state, which will be |ξ> abcde All the information is transferred to particles b, c, and d.

[0044] Among them, the CNOT (control-NOT) gate is a 2-bit quantum bit gate. Its function is that when the control bit is 1, the target bit is inverted, otherwise the target bit remains unchanged.

[0045] |ξ> abcde =|0> a (α|000>+β|011>+γ|110>+δ|101>) bcd |0> e

[0046] At this point, the overall quantum state of the system has the following form:

[0047]

[0048] Step 2: In order to transmit the unknown quantum state to the receiver Bob, the sender Alice performs Bell basis measurement on particles (b,2) and (c,5).

[0049] Among them, the four Bell bases are:

[0050] Step 3: After the Bell basis measurement, the entangled state between particles b, c, and d is converted to the entangled state between particles d, 1, 3, and 4. In order to separate particle d from the entangled state, the sender Alice performs a Hadamard gate operation on particle d and performs a single-particle measurement on particle d.

[0051] Among them, the Hadamard gate operation is:

[0052] Step 4: The sender Alice informs the receiver Bob of her measurement results through the classical channel. According to the different measurement results of the sender Alice, the receiver Bob performs corresponding unitary operations on the particles b, c, and d he owns to reconstruct the unknown GHZ-like state.

[0053] The unitary operation performed by the receiver Bob is four Pauli operators: I = |0〉〈0|+|1〉〈1|, σ x =|0><1|+|1><0|, -iσ y =|1〉〈0|-|0〉〈1|,σ z =|0〉〈0|-|1><1|.

[0054] Assume that the measurement results of sender Alice for (b,2) and (c,5) are Particles d, 1, 3, 4 will collapse to (α|0011>-β|1000>-γ|0101>+δ|1110>) d134 .

[0055] At this time, if the measurement result of the H-gate operation performed by the sender Alice on particle d is |0〉, then the particles 1, 3, and 4 owned by the receiver Bob will collapse to (α|011〉-β|000〉-γ|101〉+δ|110〉) 134 Finally, the receiver Bob executes The unknown GHZ state can be reconstructed by unitary operation.

[0056] Step 5: When the receiver Bob reconstructs (α|000〉+β|011〉+γ|110〉+δ|101〉) 134 After the GHZ state, in order to obtain the original five-particle entangled state information, two auxiliary particles are introduced: |00> fg , then execute the exchange gate on particles 1 and 3, and then execute the exchange gate on particles 1 and g.

[0057] Among them, the quantum exchange gate can operate two quantum bits, allowing the two quantum bits to exchange quantum bits with each other.

[0058] Step 6: The receiver Bob uses particles 4,3 as control bits and particles h,1 as target bits to perform two CNOT gates on (4,h)(3,1) to restore the original five-particle entangled state |ν> 134gh =(α|00000>+β|00111>+γ|11010>+δ|11101>) 134gh information, completing the unknown five-particle entangled state |ξ> abcdeThe quantum teleportation scheme of the sender Alice and the receiver Bob based on the five-particle cluster state realizes the transmission of the five-particle entangled state. The quantum circuit diagram is as follows Figure 3 shown.

[0059] Figure 3 Part I represents the operation performed by Alice before the measurement, which is to convert the five-particle entangled state to be transmitted into a three-particle GHZ-like state, reducing the consumption of quantum resources and classical resources during the transmission process. Part II is the two Bell state measurement operations performed by the communication sender Alice. Part III contains the U 134 represents the unitary operation of the communication receiver Bob, the double horizontal lines represent the classical channel, and part IV is the exchange gate and CNOT gate operations performed by the communication receiver Bob to reconstruct the initial five-particle entangled state.

[0060] Efficiency is an important factor in comparing the performance of quantum teleportation schemes, which is expressed by the formula Calculate the transmission efficiency of the protocol, where q s represents the number of quantum bits transmitted in the scheme, q u represents the number of quantum bits in the quantum channel, b t is the number of classical bits exchanged between participants.

[0061] In this embodiment, in order to send an unknown five-particle entangled state to a distant receiver Bob (q s =5), and prepared a 5-qubit cluster state (q u =5), and then the results of two Bell state measurements and one H-gate measurement (b t =4) inform the recipient Bob. Without considering the quantum resources and classical resources used for identity authentication and security checks, the quantum bit efficiency of this embodiment is This is higher than most quantum teleportation schemes. Therefore, in the present invention, the communicating parties complete the transmission of the unknown five-particle entangled state by sharing the five-particle cluster state entangled channel. The Bell state measurement, classical communication and local operation required by the whole process can all be realized, and the scheme has the characteristics of high communication efficiency.

[0062] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A teleportation method for teleporting an unknown five - particle entangled state based on a five - particle cluster state, characterized in that, it includes: The communication sender and the communication receiver share a five-particle cluster state |η> 12345 , and establish a quantum entanglement channel; The communication sender uses a CNOT gate to transform the unknown five - particle entangled state to be teleported into an unknown GHZ - like state; The communication sender performs Bell state measurement and H-gate operation on an unknown GHZ-like state based on the five-particle cluster state |η> 12345 , and then informs the communication receiver of its measurement result; The communication receiver performs a unitary operation on the particles it owns according to the measurement results of the communication sender and the five-particle cluster state |η> 12345 , and reconstructs the GHZ-like state; among them, the performed unitary operation is four Pauli operators: I = |0><0| + |1><1|, σ x = |0><1| + |1><0|, -iσ y = |1><0| - |0><1|, σ z = |0><0| - |1><1|; The communication receiver introduces two auxiliary particles |00> fg , and restores the unknown five-particle entangled state by performing two CNOT gate operations on the reconstructed GHZ-like state; The quantum circuit used by the communication sender and the communication receiver to teleport the unknown five - particle entangled state includes four parts: The first part represents that the communication sender transforms the unknown five - particle entangled state to be teleported into a three - particle GHZ - like state before measurement; the second part is two Bell - state measurement operations performed by the communication sender; the third part includes a classical channel and the unitary operation of the communication receiver; the fourth part includes the swap gate and CNOT gate operations performed by the communication receiver to reconstruct the initial five - particle entangled state.

2. The teleportation method according to claim 1, characterized in that, For the five - particle cluster state wherein, the communication sender has particles 2, 5, while the communication receiver has particles 1, 3, 4.

3. The teleportation method according to claim 2, characterized in that, During the process of the communication sender transforming the unknown five - particle entangled state to be teleported into an unknown GHZ - like state, two CNOT gate operations are performed.

4. The teleportation method according to claim 3, characterized in that, The CNOT gate is a 2 - qubit quantum gate. During the CNOT gate operation, when the control bit is 1, the target bit is inverted; otherwise, the target bit remains unchanged.

5. The teleportation method according to claim 4, characterized in that, The Bell bases used in the Bell - state measurement are:

6. The teleportation method according to claim 5, characterized in that, The operation of the H gate is as follows:

7. The teleportation method according to claim 6, characterized in that, The communication sender informs the communication receiver of its measurement results through the classical channel.

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