WO2021008508A1 - 基于中继节点测量结果随机发送的d维链式隐形传态方法 - Google Patents
基于中继节点测量结果随机发送的d维链式隐形传态方法 Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
- H04B10/70—Photonic quantum communication
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
- H04B10/07—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems
- H04B10/075—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems using an in-service signal
- H04B10/079—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems using an in-service signal using measurements of the data signal
- H04B10/0795—Performance monitoring; Measurement of transmission parameters
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
- H04B10/29—Repeaters
Definitions
- the invention relates to the field of quantum transmission, in particular to a d-dimensional chain teleportation method based on the measurement result of a relay node to be randomly sent.
- Quantum communication refers to the use of quantum channels or quantum channels supplemented by classical channels for the transmission of quantum information or classical information, including Quantum Teleportation [1-3], Quantum Dense Coding [4], Quantum Quantum Entanglement Swapping [5-7] and Quantum Secure Communication [8-12] etc.
- the theory of quantum teleportation was first proposed by Bennett, Brassard and other scientists in 1993, and used the properties of quantum entanglement to realize quantum teleportation. There have been a large number of experimental studies.
- the basic principle of quantum teleportation is: the information sender (Alice) wants to send an unknown quantum state to the information receiver (Bob), Alice and Bob share an EPR entanglement pair in advance, and implement it on the two particles held by Alice.
- quantum networking [14-16] is an inevitable development trend.
- a quantum network by introducing several relay nodes and performing entanglement exchanges between the relay nodes [17,18], the two communicating parties that do not directly share the quantum entangled pair can establish a direct entanglement channel.
- the entanglement channel can finally realize the communication between two remote nodes based on the EPR protocol.
- the research on quantum teleportation networks based on quantum relay nodes has made significant progress.
- the relay node and the information receiver may not establish a classical channel to transmit information, or the communication distance between the relay node and the information receiver is relatively long, which makes it inconvenient to transmit information.
- most of the existing multi-hop quantum teleportation methods consider the two-level situation, but in practice, the multi-level quantum state [22,23] is a very important quantum resource, and it is unknown for a multi-level quantum state.
- the teleportation of quantum states requires the establishment of a multi-level quantum teleportation channel.
- the technical problem to be solved by the present invention is to provide a d-dimensional chain teleportation method based on the measurement results of the relay node randomly sent, (1) solve the problem that the two parties in the communication network do not directly share the quantum entangled pair; (2) Solve the problem that it is difficult for relay nodes in the communication network to directly send Bell measurement results to the information receiver.
- the present invention provides a d-dimensional chain teleportation method based on the measurement results of the relay node to be randomly sent, including: the communication parties are the information sender Alice and the information receiver Bob, and the particle t carries an unknown quantum State, held by the sender Alice.
- the intermediate nodes Charliek hold particles B k and particles A k+1 , where P is a positive integer; the information receiver Bob at the target node is the P + th of the multi-hop quantum teleportation system Two nodes hold the particle B P+1 ; each adjacent node shares a two-bit Bell state quantum channel with each other, forming a chain communication channel.
- Each entangled channel has the same form and is:
- the P intermediate nodes respectively perform generalized Bell measurements on the two particles they hold to establish an entanglement channel between the information sender Alice and the information receiver Bob;
- the P intermediate nodes consider the classic channel connection with the information sender Alice and the information receiver Bob respectively, and send their generalized Bell measurement results to Alice or Bob according to the actual choice, and Alice or Bob based on the measurement they received The result determines the matrix transformation operation to be performed and adjusts the entanglement channel;
- the multi-hop teleportation system is simplified into a single-hop teleportation system, and the single-hop quantum teleportation process is performed.
- the message sender Alice performs a joint Bell measurement on the particle t and particle A 1 she owns, and sends her measurement result to the message receiver Bob. According to the received result, Bob performs the corresponding response to his particle B P+1
- the unitary operation restores the transmitted unknown quantum state information.
- P intermediate nodes consider the classical channel connection with the information sender Alice and the information receiver Bob respectively, and send their generalized Bell measurement results to Alice or Bob, Alice or Bob determines the matrix transformation operation that needs to be performed according to the measurement results he has received, and adjusts the entanglement channel;
- the adjusted quantum channel system has the following form:
- P intermediate nodes separately consider the classic channel connection with the information sender Alice and the information receiver Bob includes whether the classic information can be transmitted.
- P intermediate nodes separately consider the classical channel connection with the information sender Alice and the information receiver Bob includes transmission efficiency.
- any relay node can randomly send its own generalized Bell measurement results to the information sender Alice or the information receiver Bob, which greatly reduces The limitation of the classic channel connection.
- each relay node of the present invention can be simultaneously transmitted to the information sender Alice or the information receiver Bob, so the present invention improves the efficiency of information transmission.
- the present invention applies a high-energy entangled chain channel. Even if the sender and the receiver do not directly share the quantum entangled pair, quantum state information can still be transmitted between the two parties, which can meet the requirements of constructing a complex quantum communication network.
- Fig. 1 is a flow chart of the d-dimensional chain-type teleportation method based on the relay node measurement results randomly sent according to the present invention.
- Fig. 2 is a particle allocation diagram of the d-dimensional chain teleportation method based on the measurement results of the relay node randomly sent according to the present invention.
- Figure 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.
- FIG. 4 is a schematic diagram of particle distribution of a two-level four-hop chain teleportation method in Embodiment 1 of the present invention.
- Fig. 5 is a schematic diagram of particle distribution of the three-level three-hop chain teleportation method in the second embodiment of the present invention.
- the generalized Bell basis is the largest entangled state composed of two particles at multiple levels. It forms a complete set of orthogonal basis in the d (energy level)-dimensional Hilbert space. The specific form is as follows:
- the form of the entangled channel system of the information sender Alice and the information receiver Bob in the present invention is as follows:
- the information sender Alice and the information receiver Bob who do not directly share the entangled pair can generate a direct entangled state with the help of P intermediate nodes, establish a quantum entanglement channel, and complete the information
- the sender Alice transmits a single-particle multi-level unknown quantum state to the information receiver Bob.
- the relay node can randomly send its generalized Bell measurement results to the message sender Alice or the message receiver Bob. It includes the following steps:
- Step 1 Chain channel construction.
- the two parties in communication are the information sender Alice and the information receiver Bob.
- the particle t carries an unknown quantum state and is held by the information sender Alice.
- Alice holds the particle t and the particle A 1
- the first intermediate node Charlie1 holds the particles B 1 and A 2
- the intermediate nodes Charliek hold particles B k and particles A k+1 , where P is a positive integer
- the information receiver Bob at the target node is the P + th of the multi-hop quantum teleportation system
- Two nodes hold the particle B P+1 ; each adjacent node shares a two-bit Bell state quantum channel with each other, forming a chain communication channel.
- Each entangled channel has the same form and is:
- Step 2 Direct channel construction.
- the P intermediate nodes respectively make generalized Bell measurements on the two particles they hold. After the measurement is completed, consider the classical channel connection with the information sender Alice and the information receiver Bob (such as whether classical information transmission is possible, Whether the information communication is smooth and the transmission efficiency, etc.), send your generalized Bell measurement results to Alice or Bob according to actual choices.
- Step 3 Channel adjustment. Alice or Bob determines the matrix transformation operation that needs to be performed according to the measurement results they receive, and adjusts the entanglement channel.
- the adjusted quantum channel system has the following form:
- the direct entanglement channel of the d-dimensional multi-hop lossless quantum teleportation system can be obtained.
- the channel is composed of three parts: one is the generalized Bell measurement results of P intermediate nodes; the other is the adjustment source corresponding to each measurement result.
- the matrix transformation operation should be performed between the node and each intermediate node directly entangled state form; The third is the entangled state of the particle A 1 of the information sender Alice and the particle B P+1 of the information receiver Bob.
- Step 4 Information transfer.
- the multi-hop teleportation system is simplified into a single-hop teleportation system, and the single-hop lossless quantum teleportation process is performed.
- the message sender Alice performs a joint Bell measurement on the particle t and particle A 1 she owns, and may get 2 different measurement results:
- Alice sends her measurement results to Bob, the information receiver, and according to the received results, Bob performs the corresponding unitary operation on his particle B P+1 Recover the transmitted unknown quantum state information.
- Example 1 A d-dimensional chained teleportation method based on the measurement results of the relay node to be randomly sent. Taking two energy levels and four hops as an example, the information sender Alice transmits the unknown single event state to the information receiver Bob
- Step 1 Construct a two-level four-hop quantum teleportation chain channel.
- the two communicating parties are Alice and Bob.
- the particle t carries an unknown quantum state
- ⁇ > t c 0
- the three intermediate nodes send to Bob the information receiver.
- each entangled channel has the same form and is:
- Step 2 Direct channel construction.
- the three intermediate nodes Charlie1, Charlie2 and Charlie3 respectively make generalized Bell measurements on the two particles they hold. After the measurement is completed, consider the classic channel connection with the information sender Alice and the information receiver Bob (if it can be Perform classical information transmission, transmission efficiency, etc.), and send your generalized Bell measurement results to Alice or Bob according to actual choices.
- Direct channel construction The information sender Alice of the source node, the three intermediate nodes and the information receiver Bob as the target node perform entanglement exchange in pairs, so that Alice and Bob establish direct entanglement. Entangled channel with After the tensor product operation, the quantum states of the eight particles are expressed as:
- the three intermediate nodes Charlie1, Charlie2 and Charlie3 respectively perform Bell measurements on the two particles they hold. Each person may get four measurement results:
- Step 3 Channel adjustment. Alice performs a matrix transformation operation on particle A 1 :
- Step 4 Information transfer.
- 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.
- the message sender Alice directly entangles the channel To transmit an unknown quantum state, the quantum teleportation process is simplified to the following form:
- Embodiment 2 A d-dimensional chain teleportation method based on the measurement results of the relay node to be randomly sent, taking the three-level and three-hop as an example to realize that the information sender Alice transmits the unknown single event state to the information receiver Bob
- Step 1 Construct a three-level three-hop quantum teleportation chain channel.
- the communication parties are Alice and Bob.
- the particle t carries an unknown quantum state
- ⁇ > t c 0
- each entangled channel has the same form and is:
- Step 2 Direct channel construction.
- the two intermediate nodes Charlie1 and Charlie2 respectively make generalized Bell measurements on the two particles they hold. After the measurement is completed, consider the classic channel connection with the information sender Alice and the information receiver Bob (such as whether it can be classical Information transmission, transmission efficiency, etc.), and send your generalized Bell measurement results to Alice or Bob according to actual choices.
- Direct channel construction The information sender Alice of the source node, the three intermediate nodes and the information receiver Bob as the target node perform entanglement exchange in pairs, so that Alice and Bob establish direct entanglement. Entangled channel with After the tensor product operation, the quantum states of the six particles are expressed as:
- the two intermediate nodes Charlie1 and Charlie2 respectively perform generalized Bell measurement on the two particles they hold, and each person may get nine measurement results
- Step 3 Channel adjustment. Alice performs a matrix transformation operation on particle A 1 :
- Step 4 Information transfer.
- the multi-hop teleportation system is simplified into a single-hop teleportation system, and the single-hop lossless quantum teleportation process is performed.
- the message sender Alice directly entangles the channel To transmit an unknown quantum state, the quantum teleportation process is simplified to the following form:
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Abstract
本发明公开了一种基于中继节点测量结果随机发送的d维链式隐形传态方法。本发明基于中继节点测量结果随机发送的d维链式隐形传态方法，包括：通信双方为信息发送方Alice与信息接收方Bob，粒子t携带未知量子态，由信息发送方Alice所持有。Alice持有粒子t和粒子A 1，第1个中间节点Charlie1持有粒子B 1和A 2，第2个中间节点Charlie2持有粒子B 2和A 3，……，第k(k＝1,2,3,…,P)个中间节点Charlie k持有粒子B k和粒子A k+1。本发明的有益效果：1、本发明的基于中继节点测量结果随机发送的d维链式隐形传态方法，任一中继节点可以随机向信息发送方Alice或信息接收方Bob发送自己的广义Bell测量结果，大大降低了经典信道连接的限制。
Description
本发明涉及量子传输领域，具体涉及一种基于中继节点测量结果随机发送的d维链式隐形传态方法。
在信息的传输过程中，信息安全问题是至关重要的一点。相比于经典通信，量子通信基于量子力学理论，利用量子测不准原理和量子不可克隆定理两大量子性质保证信息传输的安全性。因此，近年来，量子通信技术逐渐成为世界范围内量子学和信息学的主要钻研热点。量子通信指利用量子信道或量子信道辅以经典信道进行量子信息或经典信息的传送，包括量子隐形传态(Quantum Teleportation)[1-3]、量子密集编码(Quantum Dense Coding)[4]、量子纠缠交换(Quantum Entanglement Swapping)[5-7]以及量子保密通信[8-12]等方面。
量子隐形传态理论最早于1993年由Bennett，Brassard等[13]几位科学家提出，并利用量子纠缠性质来实现量子隐形传态，至今已有大量的实验研究。量子隐形传态的基本原理是：信息发送方(Alice)想要向信息接收方(Bob)传送一个未知量子态，Alice与Bob事先共享一个EPR纠缠对，通过对Alice持有的两个粒子实施联合Bell基测量，由于EPR对的量子非局域关联特性，此时未知态的全部量子信息将会"转移"到EPR对的第二个粒子即Bob所持有的粒子上，只要根据经典通道传送的Bell基测量结果，对EPR对的第二个粒子的量子态施行适当的幺正变换，就可使这个粒子处于与待传送的未知态完全相同的量子态，从而在EPR的第二个粒子上实现对未知量子态的重现。
在实际的量子通信中，考虑到信道损耗，很难直接在两个距离较远的节点 之间进行隐形传态。因此，随着量子通信技术研究的深入，量子网络化[14-16]是不可避免的发展趋势。在量子网络中，通过引入若干个中继节点，并且中继节点之间两两进行纠缠交换[17,18]，就可以使没有直接共享量子纠缠对的通信双方建立起直接纠缠信道，利用这个纠缠信道，就能基于EPR协议最终实现两个远程节点之间的通信。近年来，以量子中继节点为基础量子隐形传态网络的研究取得重大进展。2005年，Sheng-Tzong Cheng等[19]提出了一种针对分级网络结构的路由机制，用来在两个没有直接共享纠缠对的节点建传送一个量子态信息；2014年，Wang Kan等[20]提出一种基于任意Bell对的量子无线多跳隐形传态体系，用以构建量子通信网络；2017年，Zhen-Zhen Zou等[21]提出了一种量子多跳隐形传态协议，该协议可以在不直接共享纠缠对的两个节点之间实现任意两量子比特态的隐形传态。但是，现有的多跳量子隐形传态方法中，中继节点的Bell测量结果都是发送给信息接收方进行处理。而实际的多跳量子隐形传态体系中，中继节点与信息接收方可能没有建立经典信道来传输信息，或者中继节点与信息接收方的通信距离较远，不便传输信息。除此之外，现有的多跳量子隐形传态方法大多数考虑两能级情况，而实际中，多能级量子态[22,23]是非常重要的量子资源，对于一个多能级未知量子态的隐形传态，需要建立多能级的量子隐形传态信道。
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发明内容
本发明要解决的技术问题是提供一种基于中继节点测量结果随机发送的d维链式隐形传态方法，(1)解决通信网络中通信双方不直接共享量子纠缠对的问题；(2)解决通信网络中中继节点难以直接向信息接收方发送Bell测量结果的问题。
为了解决上述技术问题，本发明提供了一种基于中继节点测量结果随机发送的d维链式隐形传态方法，包括：通信双方为信息发送方Alice与信息接收方Bob，粒子t携带未知量子态，由信息发送方Alice所持有。Alice持有粒子t和粒子A
1，第1个中间节点Charlie1持有粒子B
1和A
2，第2个中间节点Charlie2持有粒子B
2和A
3，……，第k(k＝1,2,3,…,P)个中间节点Charliek持有粒子B
k和粒子A
k+1，其中，P是正整数；处于目标节点的信息接收方Bob是多跳量子隐形传态系统的第P+2个节点，持有粒子B
P+1；各个相邻节点之间彼此两两共享两比特Bell态量子信道，形成链式通信信道。各纠缠信道的形式相同且为：
P个中间节点分别对自己所持有的两个粒子作广义Bell测量，以此建立信息发送方Alice与信息接收方Bob之间的纠缠信道；
P个中间节点分别考虑与信息发送方Alice和信息接收方Bob之间的经典信道连接情况，根据实际选择将自己的广义Bell测量结果发送给Alice或者Bob，Alice或Bob根据自己所接收到的测量结果确定需要执行的矩阵变换操作，调整纠缠信道；
将多跳隐形传态系统简化为单跳隐形传态系统形式，执行单跳量子隐形传态过程。信息发送方Alice对自己所拥有的粒子t和粒子A
1执行联合Bell测量，并将她的测量结果发送给信息接收方Bob，根据接收到的结果，Bob对他的粒子B
P+1执行相应的幺正操作恢复传送的未知量子态信息。
在其中一个实施例中，“P个中间节点分别考虑与信息发送方Alice和信息接收方Bob之间的经典信道连接情况，根据实际选择将自己的广义Bell测量结果发送给Alice或者Bob，Alice或Bob根据自己所接收到的测量结果确定需要执行的矩阵变换操作，调整纠缠信道；”，调整后量子信道系统有如下形式：
上式中，
表示第k个中间节点Charlie k的广义Bell测量结果，且有：
表示当Charliek对自己所拥有的粒子B
k和A
k+1测得
后，根据实际情况将测量结果发送给Alice或者Bob。令
其对应于Alice汇总接收到的测量结果后，需要对粒子A
1执行的幺正操作，其中{a}是所有将测量结果发送给Alice的中间节点标号的集合；同样地，令
其对应于Bob汇总接收到的测量结果后，需要对粒子B
P+1执行的幺正操作，{b}是所有将测量结果发送给Bob的中间节点标号的集合。
Alice和Bob执行相应的幺正操作后，可以使粒子A
1和B
P+1的纠缠态转换为
的形式。这里存在：
在其中一个实施例中，“P个中间节点分别考虑与信息发送方Alice和信息接收方Bob之间的经典信道连接情况”包括是否可以进行经典信息传输。
在其中一个实施例中，其特征在于，“P个中间节点分别考虑与信息发送方Alice和信息接收方Bob之间的经典信道连接情况”包括信息沟通是否顺畅。
在其中一个实施例中，“P个中间节点分别考虑与信息发送方Alice和信息接收方Bob之间的经典信道连接情况”包括传输效率。
本发明的有益效果：
1、本发明的基于中继节点测量结果随机发送的d维链式隐形传态方法，任一中继节点可以随机向信息发送方Alice或信息接收方Bob发送自己的广义Bell测量结果，大大降低了经典信道连接的限制。
2、本发明各个中继节点的测量结果可同时传送给信息发送方Alice或信息接收方Bob，因此本发明提高了信息传输的效率。
3、本发明应用高能级纠缠链式信道，即使发送方与接收方没有直接共享量子纠缠对，依然能在双方之间传输量子态信息，能够满足构建复杂量子通信网络的要求。
图1为本发明的基于中继节点测量结果随机发送的d维链式隐形传态方法的流程图。
图2为本发明的基于中继节点测量结果随机发送的d维链式隐形传态方法的粒子分配图。
图3为本发明信息发送方Alice、信息接收方Bob与P个中间节点进行纠缠交换建立量子信道的示意图。
图4为本发明实施例一中两能级四跳的链式隐形传态方法粒子分配示意图。
图5为本发明实施例二中三能级三跳的链式隐形传态方法粒子分配示意图。
下面结合附图和具体实施例对本发明作进一步说明，以使本领域的技术人员可以更好地理解本发明并能予以实施，但所举实施例不作为对本发明的限定。
本发明技术名词说明：
1、广义Bell基
广义Bell基是由多能级两粒子构成的最大纠缠态，它构成了d(能级数)维Hilbert空间的一组完备正交基，具体形式如下：
2、纠缠信道形式统一操作
本发明中信息发送方Alice与信息接收方Bob的纠缠信道系统形式如下：
当第k个中间节点Charliek对自己所拥有的粒子B
k和A
k+1测得
后，如果他将测量结果发送给Alice，则Alice需要对粒子A
1执行
操作；如果将测量结果发送给Bob，则Bob需要对粒子B
P+1执行
操作；当汇总所有接收到的测量结果，Alice和Bob分别执行矩阵变换
和
将粒子A
1和B
P+1的纠缠态转换为统一形式：
相关的矩阵表达式如下：
d能级链式隐形传态通信系统中，没有直接共享纠缠对的信息发送方Alice与信息接收方Bob，通过P个中间节点的帮助，能够产生直接纠缠态，建立起量子纠缠信道，完成信息发送方Alice向信息接收方Bob传送一个单粒子多能级未知量子态的过程。在这个多跳隐形传态体系中，中继节点可以随机向信息发送方Alice或信息接收方Bob发送自己的广义Bell测量结果。包括以下步骤：
步骤1：链式信道构建。通信双方为信息发送方Alice与信息接收方Bob，粒子t携带未知量子态，由信息发送方Alice所持有。Alice持有粒子t和粒子A
1，第1个中间节点Charlie1持有粒子B
1和A
2，第2个中间节点Charlie2持有粒子B
2和A
3，……，第k(k＝1,2,3,…,P)个中间节点Charliek持有粒子B
k和粒子A
k+1，其中，P是正整数；处于目标节点的信息接收方Bob是多跳量子隐形传态系统的第P+2个节点，持有粒子B
P+1；各个相邻节点之间彼此两两共享两比特Bell态量子信道，形成链式通信信道。各纠缠信道的形式相同且为：
步骤2：直接信道构建。P个中间节点分别对自己所持有的两个粒子作广义Bell测量，测量完毕之后，考虑与信息发送方Alice和信息接收方Bob之间的经典信道连接情况(如是否可以进行经典信息传输，信息沟通是否顺畅以及传输效率等)，根据实际选择将自己的广义Bell测量结果发送给Alice或者Bob。
步骤3：信道调整。Alice或Bob根据自己所接收到的测量结果确定需要执行的矩阵变换操作，调整纠缠信道。调整后量子信道系统有如下形式：
上式中，
表示第k个中间节点Charliek的广义Bell测量结果，且有：
表示当Charliek对自己所拥有的粒子B
k和A
k+1测得
后，根据实际情况(如是否可以进行经典信息传输，信息沟通是否顺畅以及传输效率等)将测量结果发送给Alice或者Bob。令
其对应于Alice汇总接收到的测量结果后，需要对粒子A
1执行的幺正操作，其中{a}是所有将测量结果发送给Alice的中间节点标号的集合；同样地，令
其对应于Bob汇总接收到的测量结果后，需要对粒子B
P+1执行的幺正操作，{b}是所有将测量结果发送给Bob的中间节点标号的集合。
Alice和Bob执行相应的幺正操作后，可以使粒子A
1和B
P+1的纠缠态转换为
的形式。这里存在：
且
至此，可以得到d维多跳无损量子隐形传态系统的直接纠缠信道，该信道由三个部分构成：一是P个中间节点的广义Bell测量结果；二是对应于各个测量结果，为调整源节点与各个中间节点直接纠缠态形式应进行的矩阵变换操作； 三是信息发送方Alice的粒子A
1与信息接收方Bob的粒子B
P+1的纠缠态。
步骤4：信息传送。将多跳隐形传态系统简化为单跳隐形传态系统形式，执行单跳无损量子隐形传态过程。信息发送方Alice对自己所拥有的粒子t和粒子A
1执行联合Bell测量，可能得到d
2种不同的测量结果：
更具体地：
实施例一：一种基于中继节点测量结果随机发送的d维链式隐形传态方法，以两能级四跳为例，实现信息发送方Alice向信息接收方Bob传送未知单粒子态|χ>
t，具体步骤：
步骤1：构建两能级四跳量子隐形传态链式信道。通信双方为Alice与Bob，粒子t携带未知量子态|χ>
t＝c
0|0>+c
1|1>，由信息发送方Alice所持有，Alice想要将该未知单粒子量子态通过三个中间节点发送给信息接收方Bob。在量子路径中，每一段纠缠信道形式相同且为：
步骤2：直接信道构建。三个中间节点Charlie1,Charlie2和Charlie3分别对自己所持有的两个粒子作广义Bell测量，测量完毕之后，考虑与信息发送方Alice和信息接收方Bob之间的经典信道连接情况(如是否可以进行经典信息传输，传输效率等)，根据实际选择将自己的广义Bell测量结果发送给Alice或者Bob。直接信道构建。源节点的信息发送方Alice、三个中间节点与作为目标节点的信息接收方Bob两两之间进行纠缠交换，使Alice与Bob建立直接纠缠。纠缠信道
和
作张量积运算，运算之后八个粒子的量子态表示为：
三个中间节点Charlie1,Charlie2和Charlie3分别对自己所持有的两个粒子执行Bell测量，每个人可能得到四种测量结果：
为了对操作过程进行详细的研究，我们以以下情况为例：中间节点Charlie1的测量结果为
将此测量结果发送给Alice；Charlie2测得结果
将此测量结果发送给Alice；Charlie3测得结果
并将结果发送给Bob。则此时系统的量子态变为
步骤3：信道调整。Alice对粒子A
1执行矩阵变换操作：
步骤4：信息传送。将多跳隐形传态系统简化为单跳隐形传态系统形式， 执行单跳无损量子隐形传态过程。信息发送方Alice通过直接纠缠信道
传送未知量子态，量子隐形传态过程简化为如下形式：
此时，Alice对其所拥有的粒子t和A
1执行Bell测量，可能得到四种测量结果
根据测量结果，Bob执行相应的幺正操作
即可恢复得到传送的未知量子态。
实施例二：一种基于中继节点测量结果随机发送的d维链式隐形传态方法，以三能级三跳为例，实现信息发送方Alice向信息接收方Bob传送未知单粒子态|χ>
t，具体步骤：
步骤1：构建三能级三跳量子隐形传态链式信道。通信双方为Alice与Bob，粒子t携带未知量子态|χ>
t＝c
0|0>+c
1|1>+c
2|2>，由信息发送方Alice所持有，Alice想要将该未知单粒子量子态通过三个中间节点发送给信息接收方Bob。在量子路径中，每一段纠缠信道形式相同且为：
步骤2：直接信道构建。两个中间节点Charlie1和Charlie2分别对自己所持有的两个粒子作广义Bell测量，测量完毕之后，考虑与信息发送方Alice和信息接收方Bob之间的经典信道连接情况(如是否可以进行经典信息传输，传输效率等)，根据实际选择将自己的广义Bell测量结果发送给Alice或者Bob。直接信道构建。源节点的信息发送方Alice、三个中间节点与作为目标节点的信息接收方Bob两两之间进行纠缠交换，使Alice与Bob建立直接纠缠。纠缠信道
和
作张量积运算，运算之后六个粒子的量子态表示为：
两个中间节点Charlie1和Charlie2分别对自己所持有的两个粒子执行广义Bell测量，每个人可能得到九种测量结果
为了对操作过程进行详细的研究，我们以以下情况为例：中间节点Charlie1的测量结果为
将此测量结果发送给Alice；Charlie2测得结果
将此测量结果发送给Bob。则此时系统的量子态变为
步骤3：信道调整。Alice对粒子A
1执行矩阵变换操作：
步骤4：信息传送。将多跳隐形传态系统简化为单跳隐形传态系统形式，执行单跳无损量子隐形传态过程。信息发送方Alice通过直接纠缠信道
传送未知量子态，量子隐形传态过程简化为如下形式：
此时，Alice对其所拥有的粒子t和A
1执行Bell测量，可能得到九种测量结果
根据测量结果，Bob执行相应的幺正操作
即可恢复得到传送的未知量子态。例如，假设Alice测得
则Bob对粒B
3子执行幺正操作
即可恢复出传送的未知量子态信息。
以上所述实施例仅是为充分说明本发明而所举的较佳的实施例，本发明的保护范围不限于此。本技术领域的技术人员在本发明基础上所作的等同替代或变换，均在本发明的保护范围之内。本发明的保护范围以权利要求书为准。
Claims (5)
- 一种基于中继节点测量结果随机发送的d维链式隐形传态方法，其特征在于，包括：通信双方为信息发送方Alice与信息接收方Bob，粒子t携带未知量子态，由信息发送方Alice所持有。Alice持有粒子t和粒子A 1，第1个中间节点Charlie1持有粒子B 1和A 2，第2个中间节点Charlie2持有粒子B 2和A 3，......，第k(k＝1,2,3,…,P)个中间节点Charliek持有粒子B k和粒子A k+1，其中，P是正整数；处于目标节点的信息接收方Bob是多跳量子隐形传态系统的第P+2个节点，持有粒子B P+1；各个相邻节点之间彼此两两共享两比特Bell态量子信道，形成链式通信信道。各纠缠信道的形式相同且为：
P个中间节点分别对自己所持有的两个粒子作广义Bell测量，以此建立信息发送方Alice与信息接收方Bob之间的纠缠信道；P个中间节点分别考虑与信息发送方Alice和信息接收方Bob之间的经典信道连接情况，根据实际选择将自己的广义Bell测量结果发送给Alice或者Bob，Alice或Bob根据自己所接收到的测量结果确定需要执行的矩阵变换操作，调整纠缠信道；此时可以建立起信息发送方Alice与信息接收方Bob之间的直接纠缠信道。将多跳隐形传态系统简化为单跳隐形传态系统形式，执行单跳量子隐形传态过程。信息发送方Alice对自己所拥有的粒子t和粒子A 1执行联合Bell测量，并将她的测量结果发送给信息接收方Bob，根据接收到的结果，Bob对他的粒子B P+1执行相应的幺正操作恢复传送的未知量子态信息。 - 如权利要求1所述的基于中继节点测量结果随机发送的d维链式隐形传态方法，其特征在于，“P个中间节点分别考虑与信息发送方Alice和信息接收方Bob之间的经典信道连接情况，根据实际选择将自己的广义Bell测量结果发送给Alice或者Bob，Alice或Bob根据自己所接收到的测量结果确定需要执行 的矩阵变换操作，调整纠缠信道；”，调整后量子信道系统有如下形式：
上式中，表示第k个中间节点Charliek的广义Bell测量结果，且有：
表示当Charliek对自己所拥有的粒子B k和A k+1测得
后，根据实际情况将测量结果发送给Alice或者Bob。令
其对应于Alice汇总接收到的测量结果后，需要对粒子A 1执行的幺正操作，其中{a}是所有将测量结果发送给Alice的中间节点标号的集合；同样地，令
其对应于Bob汇总接收到的测量结果后，需要对粒子B P+1执行的幺正操作，{b}是所有将测量结果发送给Bob的中间节点标号的集合。
Alice和Bob执行相应的幺正操作后，可以使粒子A 1和B P+1的纠缠态转换为的形式。这里存在：
- 根据权利要求1所述的基于中继节点测量结果随机发送的d维链式隐形传态方法，其特征在于，“P个中间节点分别考虑与信息发送方Alice和信息接收方Bob之间的经典信道连接情况”包括是否可以进行经典信息传输。
- 根据权利要求1所述的基于中继节点测量结果随机发送的d维链式隐形传态方法，其特征在于，“P个中间节点分别考虑与信息发送方Alice和信息接收方Bob之间的经典信道连接情况”包括信息沟通是否顺畅。
- 根据权利要求1所述的基于中继节点测量结果随机发送的d维链式隐形 传态方法，其特征在于，“P个中间节点分别考虑与信息发送方Alice和信息接收方Bob之间的经典信道连接情况”包括传输效率。
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