CN109379183B - Multi-hop lossless invisible state transfer method based on non-maximum entangled chain channel - Google Patents

Abstract

The invention relates to a multi-hop lossless teleportation method based on a non-maximum entangled chain channel. At first, Alice and Bob, both communicating parties who do not directly share a quantum entanglement pair, continuously perform entanglement exchanges with the help of p intermediate nodes, and finally A quantum entanglement channel is established to complete the multi-hop teleportation process between the sender Alice and the receiver Bob to transmit a single-particle multi-level unknown quantum state. The invention applies the non-maximum entanglement chain channel, even if the sender and the receiver do not directly share the quantum entanglement pair, quantum state information can still be transmitted between the two parties, which can meet the requirements of building a complex quantum communication network; in the multi-hop of the invention In the lossless teleportation system, if the teleportation process is successfully executed, the information receiver Bob can obtain the transmitted quantum state information; if the teleportation process fails, the information sender Alice can recover the transmitted unknown quantum state information. The unknown quantum state information is not lost.

Description

Multi-hop lossless teleportation method based on non-maximally entangled chain channel

technical field

The invention relates to a quantum communication network and an information dissemination method, in particular to a multi-hop lossless teleportation method based on a non-maximally entangled chain channel.

Background technique

Quantum informatics is an interdisciplinary subject between classical information theory and quantum mechanics, and its research fields mainly include quantum computing and quantum communication. Quantum communication is a new type of communication method that uses quantum entanglement effect to transmit information. The main body of information transmitted is quantum information or classical information, and the channel is quantum channel or quantum channel supplemented by classical channel. In recent years, with the development of quantum communication technology, quantum communication has gradually moved towards the development direction of networking. In quantum communication networks, multi-hop teleportation protocols can realize quantum teleportation between two nodes that do not directly share entangled pairs. At present, quantum communication technology has developed rapidly, and has gradually become the main research focus of quantum and informatics worldwide due to its unique advantages in terms of large communication capacity and high security.

Quantum entanglement is an indispensable physical resource in the quantum teleportation [1] system, and entanglement exchange [2-4] is a special application of the properties of quantum entanglement, which makes two pairs of entangled particles that were originally unrelated, The interaction is generated using the method of Bell measurement. The property of entanglement plays an important role in quantum communication. Quantum entanglement was originally proposed by three scientists, Einstein, Podolsky and Rosen, to prove the concept of incompleteness in quantum mechanics. In 1935, Einstein, Podolski, and Rosen proposed a thought experiment that later became known as the EPR experiment. First, prepare two particles A and B, so that the sum of some properties of these two particles (such as the spin angular momentum of electrons, the polarization of photons, etc.) is zero, but the properties of a single particle are uncertain, such a Pairs of particles, called EPR pairs, are in an entangled state because the properties of the two particles are closely linked. Then the two particles are separated by any distance in space, and the state of particle A is measured at this time. If the measurement result is "0", then the state of B can be immediately obtained as "1". EPR believes that there is a "spooky action at a distance" between the entangled particles A and B.

The concept of quantum teleportation was proposed by several scientists such as Bennett, Brassard, etc. [5] in 1993, and used the properties of quantum entanglement to realize quantum teleportation, thus creating a precedent for quantum teleportation research. The basic principle of quantum teleportation is: joint Bell basis measurement is performed between the unknown quantum state to be transmitted and one of the particles of the EPR entanglement pair. "Transfer" to the second particle of the EPR pair, as long as the quantum state of the second particle of the EPR pair is subjected to an appropriate unitary transformation according to the Bell basis measurements transmitted by the classical channel, this particle can be placed in the same The transmitted unknown state is exactly the same quantum state, thereby realizing the reconstruction of the unknown quantum state on the second particle of the EPR. In 1997, the Austrian Zeilinger group completed the first indoor experimental verification of quantum teleportation, which became a classic work in the field of quantum information experiments.

With the deepening of quantum communication research, networking is an inevitable development trend, and quantum relay nodes in quantum communication networks [6,7] have therefore received extensive attention. In the quantum relay node scheme, there are many intermediate nodes between the sending node and the receiving node. Every two adjacent nodes are connected by an entangled channel to form a chain channel. All nodes (including the sending node and the receiving node) The letter node) exchanges entanglement with its adjacent nodes, and performs Bell measurement on the particles it owns to obtain an entangled state. Finally, the entangled state between the sender node and the receiver node can be established. Using this entanglement state, Based on the EPR protocol, the communication between the two nodes can finally be realized. In recent years, major breakthroughs have been made in the theoretical research of quantum teleportation based on quantum relay nodes. In 2005, Sheng-Tzong Cheng et al. [8] proposed a routing mechanism for hierarchical network structure to transmit a quantum state information between two nodes that do not directly share entangled pairs; in 2014, Wang Kan et al. [9] ] A quantum wireless multi-hop teleportation system based on any Bell pair is proposed to construct a quantum communication network. However, most of the existing multi-hop quantum teleportation methods [10, 11] are probabilistic teleportation, and the successful transmission of unknown quantum states has a certain probability. Once the transmission fails, the unknown quantum state information will be lost, resulting in the loss of quantum resources It is wasteful, and some methods of realizing quantum lossless [12] teleportation systems have not been extended to the field of quantum networks.

Multi-level quantum states [13, 14] are very important quantum resources in quantum information and quantum computing. For the teleportation of a multi-level unknown quantum state, a multi-level quantum teleportation channel needs to be established to execute In the teleportation process, quantum operations such as two-level CNOT gate operations, H gate operations, and Bell measurements should be extended to multi-level generalized CNOT gate operations, generalized H gate operations, and generalized Bell measurements. Yan Xia et al. [15] realized a generalized teleportation system by transmitting multi-bit unknown quantum state information based on d-level N particle GHZ channel; Ping Zhou et al. [16] proposed a d-dimensional quantum system based on non-maximally entangled quantum channel Multi-party controlled teleportation for extending quantum teleportation to multi-level forms. These d-level quantum teleportation methods are also probabilistic teleportation. If the teleportation process fails, the unknown quantum state information to be transmitted cannot be preserved.

References of the present invention are as follows:

[1]YANG C P,GUO G C.Multi-particle generalization of teleportation[J].Chin Phys Lett,2000,17:162.

[2] PAN J W, BOUWMEESTER D, WEINFURTER H, et a1. Experimental entanglementswapping: Entangling photons that never interacted [J]. Physical Review Letters, 1998, 80(18): 3891-3894.

[3]LU H,GUO G C.Teleportation of two-particle entangled state viaentanglement swapping[J].Phys LettA,2000,276:209.

[4] M.A.Sol'1s-Prosser, A.Delgado, O.Jim'enez, and L.Neves. Deterministic and probabilistic entanglement swapping of nonmaximally entangled states assisted by optimal quantum state discrimination[J].PHYSICAL REVIEW A 89,012337(2014 ).

[5]Bennett C.H.Brassard G, Crepeau C, et al.Teleporting an UnknownQuantum State via Dual Classical and Einstein-Podolsky-Rosen Channels[J],Phys.Rev.Lett.,1993,70:1895-1899.

[6] Xiu-Bo Chen, Yuan Su, Gang Xu, Ying Sun, Yi-Xian Yang. Quantum statesecure transmission in network communications[J]. Information Sciences 276(2014) 363-376.

[7]Zhen-Zhen Li,Gang Xu,Xiu-Bo Chen,Xingming Sun,and Yi-XianYang.Multi-User Quantum Wireless Network Communication Based on Multi-QubitGHZ State[J].IEEE COMMUNICATIONS LETTERS,VOL.20,NO .12, DECEMBER 2016.

[8] Sheng-Tzong Cheng, Chun-Yen Wang, Ming-Hon Tao.Quantum communication for wireless wide-area networks[J],IEEE.Journal on SelectedAreas inCommunications,2005,23(7):1424-1432.

[9] Kan Wang, Xu-Tao Yu, Sheng-Li Lu, Yan-Xiao Gong.Quantum wirelessmultihop communication based on arbitrary Bell pairs and teleportation.[J].Physical ReviewA, 2014,89(2A):1-10.

[10]Zhen-Zhen Zou,Xu-Tao Yu,Yan-Xiao Gong,Zai-Chen Zhang.Multihopteleportation of two-qubit state via the composite GHZ-Bell channel[J].Physical ReviewA,2017,381(2): 76-81.

[11]Meiyu Wang,Fengli Yan.General probabilistic chain teleportation[J].Optics Communications 284(2011)2408–2411.

[12]Luis Roa,Caspar Groiseau.Probabilistic teleportation without lossof information[J].Phys.Rev.A(3),2015,91(1):012344.

[13] Zheng Yuhong, Zhao Suqian, Du Zhanle, Yan Fengli. Transport of multi-level multi-particle quantum states. Journal of Hebei Normal University (Natural Science Edition), Vol.26No.2, Mar.2002.

[14] CAO Min, ZHU Shi-Qun. Probabilistic Teleportation of Multi-particled-Level Quantum State[J]. Communications in Theoretical Physics. 2005, Vol.43(5):803–805.

[15] Yan Xia, Jie Song, He-Shan Song, Bo-Ying Wang. Generalized Teleportation of a d-Level N-Particle GHZ State with One Pair of Entangled Particles as the Quantum Channel [J]. Int J Theor Phys (2008) 47:2835 –2840.

[16] Ping Zhou, Xi-Han Li, Fu-Guo Deng, Hong-Yu Zhou. Multiparty-controlled teleportation of an arbitrary m-qudit state with pure entangled quantum channel [J], Journal of Physics, 2007, 40(43): 13121-13130.

SUMMARY OF THE INVENTION

Based on this, the present invention provides a multi-hop lossless teleportation method based on a non-maximally entangled chain channel, which solves the problem that the two communicating parties do not directly share entangled pairs in a communication network. Moreover, in this multi-hop lossless teleportation system, if the teleportation process is successfully executed, the information receiver Bob can obtain the transmitted quantum state information; if the teleportation process fails, the information sender Alice can recover the transmitted quantum state information. Unknown quantum state information, the unknown quantum state information will not be lost. It includes the following steps:

Step 1: Chain channel construction. The two communicating parties are the information sender Alice and the information receiver Bob. The particle src carries an unknown quantum state, which is held by the information sender Alice. The sender Alice holds particle src and particle 1, the first intermediate node holds particle 2 and particle 3, the second intermediate node holds particle 4 and particle 5... i (i=1,2,3,... ,p) intermediate nodes hold particle 2i and particle 2i+1, where p is a positive integer; Bob, the information receiver at the target node, is the p+2th node of the multi-hop quantum teleportation system, holding particle 2p +2; each adjacent node shares two-bit Bell state quantum channels with each other to form a chain communication channel; the form of each entangled channel is:

Step 2: Direct channel construction. The p intermediate nodes perform generalized Bell measurements on the two particles they own, so that a two-particle entanglement channel is formed between the information sender Alice and the information receiver Bob, and the entangled state is in the form of:

Step 3: Channel adjustment. The p intermediate nodes respectively send their own generalized Bell measurement results to the information receiver Bob, and Bob determines the matrix transformation operation that needs to be performed on the channel according to the p measurement results, and adjusts the entangled channel. The adjusted quantum channel system has the following form:

表示第i个中间节点的广义Bell测量结果，

表示当第i个中间节点对自己所拥有的粒子2i和2i+1测得

后，需要对粒子1和粒子2i+2的纠缠态实施

操作，使这两个粒子的纠缠态转换为

的形式。

是矩阵变换

的逆变换操作。信息发送方Alice的粒子1与接收方Bob的粒子2p+2的纠缠态为：in,

represents the generalized Bell measurement of the ith intermediate node,

Indicates that when the i-th intermediate node measures the particles 2i and 2i+1 it owns

After that, the entangled state of particle 1 and particle 2i+2 needs to be implemented

operation, so that the entangled state of the two particles is converted into

form.

is the matrix transformation

inverse transform operation. The entangled state of the particle 1 of the sender Alice and the particle 2p+2 of the receiver Bob is:

的取值与

和第i+1个中间节点的广义Bell测量结果有关。假设第i+1个中间节点的测量结果为

则存在：channel parameters

The value of and

It is related to the generalized Bell measurement result of the i+1th intermediate node. Suppose the measurement result of the i+1th intermediate node is

then exists:

So far, the channel form of the d-level multi-hop lossless quantum teleportation system can be obtained. The channel consists of three parts: one is the generalized Bell measurement results of p intermediate nodes; the other is corresponding to each measurement result, which is the adjustment source. The matrix transformation operation that should be performed in the form of direct entanglement between the node and each intermediate node; the third is the entangled state of the particle 1 of the information sender Alice and the particle 2p+2 of the information receiver Bob.

Step 4: Information transmission. The multi-hop teleportation system is simplified to the form of a single-hop teleportation system, and the single-hop lossless quantum teleportation process is performed; an auxiliary particle |0> _e is introduced into the system, which is held by the information receiver Bob, and the process is carried out simultaneously. The following two operations: (1) Alice, the information sender, performs generalized CNOT and generalized H-gate operations on the particle src and particle 1 it owns; (2) The information receiver Bob holds the particle 2p+2 and the auxiliary particle. e performs a two-bit state unitary operation

Step 5: Information reception or information retention. The information receiver Bob measures the auxiliary particle e. If the measurement result is |0> _e , the information sender Alice then measures the particle src and particle 1 it owns under the basis |0> and |1>, respectively. The measurement result is sent to the information receiver Bob, and Bob performs the corresponding unitary operation to recover the unknown quantum state transmitted; if the measurement result is |1> _e , the information sender Alice performs the operation on the particle src and particle 1 it owns. The operation of generalized H gate and generalized CNOT gate, thus preserving the unknown quantum state information to be transmitted.

It is characterized in that: in the multi-hop lossless teleportation system, if the teleportation process is successfully executed, the information receiver Bob can obtain the transmitted quantum state information; if the teleportation process fails, the information sender Alice can recover Unknown quantum state information transmitted, the unknown quantum state information will not be lost. Due to the application of the above-mentioned technical solutions, the present invention has the following advantages compared with the prior art:

1. The multi-hop lossless quantum teleportation method of the present invention, because the information receiver Bob introduces an auxiliary particle |0> _e , can retain the unknown quantum state information to be transmitted when the teleportation is unsuccessful, and will not cause quantum loss of resources.

2. The measurement results of each intermediate node of the present invention can be simultaneously transmitted to the information receiver Bob, so the present invention improves the efficiency of information transmission.

3. The present invention applies the non-maximum entanglement chain channel, even if the sender and the receiver do not directly share the quantum entanglement pair, quantum state information can still be transmitted between the two parties, which can meet the requirements of building a complex quantum communication network.

Description of drawings

FIG. 1 is a flow chart of a multi-hop lossless teleportation method based on a non-maximally entangled chain channel of the present invention.

FIG. 2 is a particle allocation diagram of the multi-hop lossless teleportation method based on the non-maximally entangled chain channel of the present invention.

FIG. 3 is a schematic diagram of the information sender Alice, the information receiver Bob and p intermediate nodes performing entanglement exchange to establish a quantum channel according to the present invention.

FIG. 4 is a schematic diagram of particle allocation in the lossless teleportation method with two energy levels and two hops in Embodiment 1 of the present invention.

FIG. 5 is a schematic diagram of particle allocation in a three-level single-hop lossless teleportation method in Embodiment 2 of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

Description of the technical terms of the present invention:

1. Generalized Bell basis

The generalized Bell basis is the largest entangled state composed of two particles with multiple energy levels, and it constitutes a set of complete orthonormal basis of d (energy level)-dimensional Hilbert space. The specific form is as follows:

2. Z-based measurement

The Z-based measurement is a projection measurement carried out in the ground state of the single-bit particle, and the ground state of the single-bit particle at the d level is: |m>(m=0,1,2,...,d-1).

3. Generalized controlled NOT gate

A quantum generalized controlled NOT gate (CNOT gate) is a typical multi-qubit quantum logic gate, which has two input qubits, the control qubit and the target qubit. Its function is: the control qubit remains unchanged, and the target qubit is the result of the modulo d addition of the control qubit and the target qubit. The matrix form corresponding to the two-level controlled NOT gate is:

Extending the input two qubits to the d level, the corresponding expression of the generalized controlled NOT gate is:

4. Generalized H gate

In the present invention, the d-level H gate operation will be used, and the specific form is as follows:

5. Unified operation in the form of entangled channels

The entangled channel system form of the information sender Alice and the information receiver Bob in the present invention is as follows:

后，需要对粒子1和粒子2i+2的纠缠态实施

操作，使这两个粒子的纠缠态转换为统一形式：

的矩阵表达式如下：When the i-th intermediate node measures the particles 2i and 2i+1 it owns

After that, the entangled state of particle 1 and particle 2i+2 needs to be implemented

operation to convert the entangled state of these two particles into a unified form:

The matrix expression for is as follows:

6. The joint unitary operation of the particle 2p+2 owned by the information receiver Bob and the auxiliary particle e

After the invention determines the d-level multi-hop lossless quantum teleportation system channel, the entangled state of the particle 1 of the information sender Alice and the particle 2p+2 of the information receiver Bob has the following representation:

且P₀＝min{P₀,P₁,P₂,…,P_d-1}。本发明中步骤4将多跳无损隐形传态系统简化为单跳无损隐形传态系统形式，执行单跳无损量子隐形传态过程，需要在系统中引入一个由信息接收方Bob持有的辅助粒子|0>_e，并执行幺正操作

幺正操作

的形式表示如下：Assume

And P ₀ =min{P ₀ , P ₁ , P ₂ , . . . , P _d-1 }. Step 4 in the present invention simplifies the multi-hop lossless teleportation system into the form of a single-hop lossless teleportation system, and to perform the single-hop lossless quantum teleportation process, it is necessary to introduce an auxiliary particle held by the information receiver Bob into the system |0> _e , and perform a unitary operation

Unitary operation

is expressed in the form of:

In the chain lossless teleportation communication system, the information sender Alice and the information receiver Bob who do not directly share entangled pairs can generate quantum entangled states with the help of p intermediate nodes, establish a quantum entanglement channel, and complete the information sender. The process in which Alice transmits a single-particle multi-level unknown quantum state to the information receiver Bob. In this multi-hop lossless teleportation system, if the teleportation process is successfully executed, the information receiver Bob can obtain the transmitted quantum state information; if the teleportation process fails, the information sender Alice can recover the transmitted unknown quantum state information. state information, the unknown quantum state information will not be lost. Include the following steps:

Step 1: Chain channel construction. The two communicating parties are the information sender Alice and the information receiver Bob. The particle src carries an unknown quantum state, which is held by the information sender Alice. The sender Alice holds particle src and particle 1, the first intermediate node holds particle 2 and particle 3, the second intermediate node holds particle 4 and particle 5... i (i=1,2,3,... ,p) intermediate nodes hold particle 2i and particle 2i+1, where p is a positive integer; Bob, the information receiver at the target node, is the p+2th node of the multi-hop quantum teleportation system, holding particle 2p +2; each adjacent node shares two-bit Bell state quantum channels with each other to form a chain communication channel; the form of each entangled channel is:

Step 2: Direct channel construction. The p intermediate nodes make generalized Bell measurements on the two particles they own, so that a two-particle entanglement channel is formed between the information sender Alice and the information receiver Bob, and the entangled state is in the form of:

Step 3: Channel adjustment. The p intermediate nodes respectively send their own generalized Bell measurement results to the information receiver Bob, and Bob determines the matrix transformation operation that needs to be performed on the channel according to the p measurement results, and adjusts the entangled channel. The adjusted quantum channel system has the following form:

表示第i个中间节点的广义Bell测量结果，

表示当第i个中间节点对自己所拥有的粒子2i和2i+1测得

后，需要对粒子1和粒子2i+2的纠缠态实施

操作，使这两个粒子的纠缠态转换为

的形式。

是矩阵变换

的逆变换操作。信息发送方Alice的粒子1与接收方Bob的粒子2p+2的纠缠态为：in,

represents the generalized Bell measurement of the ith intermediate node,

Indicates that when the i-th intermediate node measures the particles 2i and 2i+1 it owns

After that, the entangled state of particle 1 and particle 2i+2 needs to be implemented

operation, so that the entangled state of the two particles is converted into

form.

is the matrix transformation

inverse transform operation. The entangled state of the particle 1 of the sender Alice and the particle 2p+2 of the receiver Bob is:

的取值与

和第i+1个中间节点的广义Bell测量结果有关。假设第i+1个中间节点的测量结果为

则存在：channel parameters

The value of and

It is related to the generalized Bell measurement result of the i+1th intermediate node. Suppose the measurement result of the i+1th intermediate node is

then exists:

So far, the channel form of the d-level multi-hop lossless quantum teleportation system can be obtained. The channel consists of three parts: one is the generalized Bell measurement results of p intermediate nodes; the other is corresponding to each measurement result, which is the adjustment source. The matrix transformation operation that should be performed in the form of direct entanglement between the node and each intermediate node; the third is the entangled state of the particle 1 of the information sender Alice and the particle 2p+2 of the information receiver Bob.

Step 4: Information transmission. The multi-hop teleportation system is simplified to the form of a single-hop teleportation system, and the single-hop lossless quantum teleportation process is performed; an auxiliary particle |0> _e is introduced into the system, which is held by the information receiver Bob, and the process is carried out simultaneously. The following two operations: (1) Alice, the information sender, performs generalized CNOT and generalized H-gate operations on the particle src and particle 1 it owns; (2) The information receiver Bob holds the particle 2p+2 and the auxiliary particle. e performs a two-bit state unitary operation

Step 5: Information reception or information retention. The information receiver Bob measures the auxiliary particle e. If the measurement result is |0> _e , the information sender Alice then measures the particle src and particle 1 it owns under the basis |0> and |1>, respectively. The measurement result is sent to the information receiver Bob, and the information receiver Bob performs the corresponding unitary operation to recover the unknown quantum state transmitted; if the measurement result is |1> _e , the information sender Alice has the particles src and Particle 1 performs the operations of the generalized H gate and the generalized CNOT gate, thereby retaining the unknown quantum state information to be transmitted.

More specifically:

Embodiment 1: A multi-hop lossless teleportation method based on a non-maximally entangled chain channel, taking two energy levels and two hops as an example, the information sender Alice transmits the unknown single-particle state |χ> _src to the information receiver Bob ,Specific steps:

中间节点与接收方Bob的纠缠信道为：

Step 1: Construct a two-level two-hop quantum lossless teleportation chain channel. The two communicating parties are Alice and Bob. The particle src carries the unknown quantum state |χ> _src =c ₀ |0>+c ₁ |1>, which is held by the information sender Alice, who wants to pass the unknown single-particle quantum state through An intermediate node sends the message to Bob, the receiver of the message. The entangled channel between the sender Alice and the intermediate node is:

The entangled channel between the intermediate node and the receiver Bob is:

与

作张量积运算，运算之后四个纠缠粒子的态表示为：Step 2: Direct channel construction. The source node's information sender Alice, the intermediate node and the target node's information receiver Bob exchange entanglement, so that Alice and Bob establish a quantum entanglement channel. entangled channel

and

For the tensor product operation, the states of the four entangled particles after the operation are expressed as:

The intermediate node performs joint Bell measurement on particle 2 and particle 3 it owns, and may obtain four measurement results. Correspondingly, particles 1 and 4 will collapse into four entangled states:

为例，则Alice的粒子1和Bob的粒子4坍塌到纠缠态：There are four kinds of Bell measurement results for particle 2 and particle 3 owned by the intermediate node, and the measurement results are

For example, Alice's particle 1 and Bob's particle 4 collapse into an entangled state:

|φ ₁₁ > ₁₄ = [a ₂₁ a ₁₀ |01>-a ₂₀ a ₁₁ |10>] ₁₄

Step 3: Channel adjustment. Perform the matrix transformation operation: U ₁₁ =|1><0|+e ^πi |0><1| After that, the entangled state form becomes |Φ> ₁₄ =[a ₂₀ a ₁₁ |00>+a ₂₁ a ₁₀ |11 >] ₁₄ , then the entire system channel is expressed as:

Step 4: Information transmission. Let a ₂₀ a ₁₁ =P ₀ and a ₂₁ a ₁₀ =P ₁ . The two-hop lossless teleportation system is simplified to the form of a single-hop lossless teleportation system, and the single-hop lossless quantum teleportation process is performed. Introducing an auxiliary particle |0> _e into the system, which is held by the receiver Bob, the lossless teleportation system becomes the following form:

两项操作执行完毕后，无损隐形传态系统变为如下形式：Step 5: Information reception or information retention. Perform the following two operations at the same time: (1) Alice performs CNOT and H gate operations on the particle src and particle 1 she owns; (2) Bob performs a unitary operation on the particle 2p+2 and the auxiliary particle e she holds

After the two operations are performed, the lossless teleportation system becomes as follows:

Bob measures the auxiliary particle e, and may get two different measurement results: |0> _e and |1> _e . When the measurement result is |0> _e , that is

Then Alice performs Z-based measurement on the particle src and particle 1 she owns in the ground state |00>, |01>, |10>, |11>, and sends the measurement result to Bob, who executes the corresponding unitary The operation restores the teleported unknown particle state.

When the measurement result is |1> _e , that is

Alice performs H gate and CNOT gate operations on the particle src and particle 1 she owns, so as to retain the unknown particle state information to be transmitted, and the unknown quantum substate information will not be lost.

Embodiment 2: A multi-hop lossless teleportation method based on a non-maximally entangled chain channel, taking a three-level single hop as an example, the information sender Alice transmits an unknown single-particle state |χ> _src to the information receiver Bob ,Specific steps:

Step 1: Build a three-level single-hop lossless quantum teleportation model. The two communicating parties are Alice and Bob. The particle src carries an unknown quantum state |χ> _src =c ₀ |0>+c ₁ |1>+c ₂ |2>, which is held by the sender Alice, who wants to make the unknown quantum state |χ> src =c 0 |0>+c 1 |1>+c 2 |2> The single-particle quantum state is sent directly to the receiver Bob. The entangled channel between the sender Alice and the intermediate node is:

Step 2: Perform a single-hop lossless quantum teleportation process. Introducing an auxiliary particle |0> _e into the system, which is held by the information receiver Bob, the lossless teleportation system becomes the following form:

两项操作执行完毕后，无损隐形传态系统变为如下形式：Step 3: Set a ₁₀ =min{a ₁₀ ,a ₁₁ ,a ₁₂ } to perform the following two operations at the same time: (1) Alice performs generalized CNOT gate and generalized H gate operations on the particle src and particle 1 she owns; ( 2) Bob performs a unitary operation on the particle 2 he holds and the auxiliary particle e

After the two operations are performed, the lossless teleportation system becomes as follows:

Step 4: Bob measures the auxiliary particle e, and may obtain two different measurement results: |0> _e and |1> _e . When the measurement result is |0> _e , that is

Then Alice can perform Z-based measurement on the particle src and particle 1 it owns, and send the measurement result to Bob, who performs the corresponding unitary operation U _sr to restore the transmitted unknown particle state; when the measurement result is |1> _e , i.e.

Then Alice performs the operations of the generalized H gate and the generalized CNOT gate on the particle src and the particle 1 it owns, so as to retain the information of the unknown particle state to be transmitted, and the information of the unknown quantum substate will not be lost.

The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity, all possible combinations of the technical features in the above-described embodiments are not described. However, as long as there is no contradiction between the combinations of these technical features, All should be regarded as the scope described in this specification.

The above-mentioned embodiments only represent several embodiments of the present invention, and the descriptions thereof are specific and detailed, but should not be construed as a limitation on the scope of the invention patent. It should be pointed out that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can also be made, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention should be subject to the appended claims.

Claims (1)

1. a kind of multi-hop lossless teleportation method based on non-maximum entangled chain channel, is characterized in that, comprises: The two communicating parties are the information sender Alice and the information receiver Bob. The particle src carries the unknown quantum state and is held by the information sender Alice; the sender Alice holds the particle src and the particle 1, and the first intermediate node holds the particles 2 and 2. Particle 3, the second intermediate node holds particle 4 and particle 5... The i-th intermediate node holds particle 2i and particle 2i+1, where i=1,2,3,...,p, p is a positive integer; The information receiver Bob at the target node is the p+2th node of the multi-hop quantum teleportation system, and holds the particle 2p+2; each adjacent node shares the two-bit Bell state quantum channel with each other to form a chain communication channel; the form of each entangled channel is:

Among them, i=1,2,3,...,p+1; The p intermediate nodes make generalized Bell measurements on the two particles they own, so that a two-particle entanglement channel is formed between the information sender Alice and the information receiver Bob; The p intermediate nodes respectively send their own generalized Bell measurement results to the information receiver Bob, and Bob determines the matrix transformation operation to be performed according to the p measurement results, and adjusts the entangled channel; Simplify the multi-hop teleportation system into the form of a single-hop teleportation system, and perform a single-hop lossless quantum teleportation process; introduce an auxiliary particle e into the system, which is held by the information receiver Bob; perform the following two at the same time Operation: (1) Alice, the information sender, performs generalized CNOT and generalized H-gate operations on the particle src and particle 1 it owns; (2) Bob, the information receiver, performs two operations on the particle 2p+2 and the auxiliary particle e it holds. bit state unitary operation; The information receiver Bob measures the auxiliary particle e. If the measurement result is |0> _e , the information sender Alice then measures the particle src and particle 1 it owns under the basis |0> and |1>, respectively. The measurement result is sent to the information receiver Bob, and Bob performs the corresponding unitary operation to recover the unknown quantum state transmitted; if the measurement result is |1> _e , the information sender Alice performs the operation on the particle src and particle 1 it owns. Operation of generalized H gate and generalized CNOT gate, so as to retain the unknown quantum state information to be transmitted; In "p intermediate nodes send their own generalized Bell measurement results to the information receiver Bob, Bob determines the matrix transformation operation to be performed according to the p measurement results, and adjusts the entangled channel", the adjusted quantum channel system has the following form:

in,

Among them, i=1, 2, 3, ..., p, representing the generalized Bell measurement result of the i-th intermediate node

Indicates that when the i-th intermediate node measures the particles 2i and 2i+1 it owns

Then, i=1, 2, 3,...,p, it is necessary to implement the entangled state of particle 1 and particle 2i+2

operation, i = 1, 2, 3, ..., p, so that the entangled state of these two particles is transformed into

form;

is the matrix transformation

The inverse transform operation of , i=1,2,3,...,p; the entangled state of the particle 1 of the information sender Alice and the particle 2p+2 of the information receiver Bob is:

channel parameters

The value of and

It is related to the generalized Bell measurement result of the i+1th intermediate node, where i=1,2,3,...,p; The specific form of the generalized H gate:

The form of the unitary operation performed by the information receiver Bob on the particle 2p+2 he holds and the auxiliary particle e is expressed as follows:

in,

And P ₀ =min{P ₀ , P ₁ , P ₂ , . . . , P _d-1 }.

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