WO2023115696A1 - 信道调制权转移的高维多跳无损隐形传送方法 - Google Patents

信道调制权转移的高维多跳无损隐形传送方法 Download PDF

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WO2023115696A1
WO2023115696A1 PCT/CN2022/078320 CN2022078320W WO2023115696A1 WO 2023115696 A1 WO2023115696 A1 WO 2023115696A1 CN 2022078320 W CN2022078320 W CN 2022078320W WO 2023115696 A1 WO2023115696 A1 WO 2023115696A1
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modulation
node
channel
terminal
measurement
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汪澳
姜敏
丁祎
刘芹
苗天宇
孙兵
陈虹
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Suzhou University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0852—Quantum cryptography
    • H04L9/0855—Quantum cryptography involving additional nodes, e.g. quantum relays, repeaters, intermediate nodes or remote nodes
    • 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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0852—Quantum cryptography

Definitions

  • the invention relates to the technical field of communication network and information dissemination, in particular to a high-dimensional multi-hop lossless teleportation method for channel modulation right transfer.
  • quantum communication theory includes three main branches: Quantum Key Distribution (Quantum Key Distribution, QKD), Quantum Secure Direct Communication (Quantum Secure Direct Communication, QSDC) and Quantum Teleportation (Quantum Teleportation, QT).
  • QKD Quantum Key Distribution
  • QSDC Quantum Secure Direct Communication
  • QT Quantum Teleportation
  • the purpose of quantum secure direct communication is to transmit classical messages between communicators by means of quantum channels, and correspondingly, directly transmit quantum states between communicators.
  • Bennett and other scholars first proposed the concept of quantum teleportation, that is, the two parties in the communication share entangled pairs, and the sending terminal can transmit the unknown quantum state to another particle at the far end without sending the particle itself.
  • the Austrian Zeilinger research group first successfully demonstrated quantum teleportation experimentally. Since then, this emerging theory has quickly become a research hotspot in the field of quantum communication, and various teleportation methods and experiments have been successively studied. propose.
  • Quantum teleportation plays an important role in quantum communication and quantum information, and it represents an essential element in the development of many quantum technologies, such as quantum repeaters, quantum gate teleportation, measurement-based computing, and port-based quantum teleportation state etc.
  • the process of quantum teleportation is as follows: first, the sender Alice and the receiver Bob share a Bell channel with maximum entanglement; then, Alice performs a joint measurement on her two particles based on Bell, and informs Bob of the result; Based on the measurements, Bob performs one of four unitary operations on his particles to recover the original information. If Alice is able to distinguish all four possible measurements, the transfer process can in principle be completed with a 100% success rate, which is called deterministic transfer.
  • Deterministic quantum teleportation typically relies on maximally entangled channels. However, in realistic teleportation scenarios, most channels can easily evolve from maximally entangled states to non-maximally entangled states due to the inevitable coupling effects between quantum states and their surroundings. This will increase the risk of information loss and reduce the fidelity of the channel.
  • probabilistic teleportation schemes were proposed, which used various non-maximally entangled states as quantum channels, such as Einstein-Podolsky-Rosen (EPR) states, cluster states, W states, and mixed states, etc. .
  • EPR Einstein-Podolsky-Rosen
  • Li et al. proposed a probabilistic teleportation scheme, using multiple non-maximally entangled Bell states as quantum channels to transmit unknown quantum states.
  • Chen et al. proposed a probabilistic teleportation protocol with multiple partially entangled Bell states to teleport unknown multiparticle GHZ states.
  • Gao et al. proposed a scheme to use two three-particle entangled W states as quantum channels to transmit unknown three-particle W states.
  • the technical problem to be solved by the present invention is to overcome the lack of a teleportation method in the prior art to solve the non-maximal entanglement evolution problem of the maximum entanglement channel in the quantum communication network and the difficulty of implementing high-dimensional multi-particle unitary operations.
  • the present invention provides a high-dimensional multi-hop lossless teleportation method that realizes channel modulation right transfer by a system.
  • the system includes a sending terminal, a receiving terminal and several intermediate nodes.
  • the method includes:
  • any intermediate node with high-dimensional modulation capability among several intermediate nodes as a modulation node, and determining the GHZ channel between the sending terminal and the modulation node and the GHZ channel between the modulation node and the receiving terminal channel;
  • the information to be transmitted is sent by the sending terminal to the receiving terminal;
  • the modulation node introduces auxiliary particles to perform a unitary operation to modulate the channel. If the channel modulation is successful, the transmitting terminal, the modulating node and the intermediate node perform a measurement operation, and send the measurement result to the receiving terminal. The receiving terminal performs unitary transformation to recover the information to be transmitted, and if the channel modulation fails, the transmitting terminal recovers the information to be transmitted.
  • determining the GHZ channel between the sending terminal and the modulation node includes:
  • An intermediate node between the transmitting terminal and the modulating node performs generalized Bell state measurement and GH measurement, and sends the measurement results to the transmitting terminal, and the transmitting terminal performs a unitary operation to construct the transmitting terminal and the GHZ channels between the modulation nodes described above.
  • determining the GHZ channel between the modulation node and the receiving terminal includes:
  • the intermediate node between the modulation node and the receiving terminal performs generalized Bell state measurement and GH measurement, and sends the measurement results to the modulation node, and the modulation node performs a unitary operation to construct the modulation node and GHZ channel between the receiving terminals.
  • the two non-maximally entangled states connecting the sending terminal, the modulating node and the receiving terminal are as follows:
  • the modulation node while the information to be transmitted is sent from the sending terminal to the receiving terminal, the modulation node performs unitary operation to perform channel modulation, including:
  • the sending terminal performs Bell measurement on the particles held by it, and performs GH operation on the particles held by the modulation node and the intermediate node, and at the same time, the modulation node performs unitary operation on the particles held by it Channel modulation is performed, wherein the particles held by the modulation node include the introduced auxiliary particles.
  • the modulation node introduces auxiliary particles to perform unitary operations to modulate the channel, including:
  • the modulation node performs a measurement operation on the auxiliary particle under the basis ⁇
  • the modulation node performs a measurement operation on the auxiliary particle under the basis ⁇
  • the modulation node and the intermediate node respectively perform GH measurement on the particles they hold, and at the same time, the modulation node performs Bell measurement on the particles it holds to obtain a second measurement result;
  • the first measurement result and the second measurement result are sent to the receiving terminal, and the receiving terminal performs unitary transformation to recover the information to be transmitted.
  • the modulation node performs a measurement operation on the auxiliary particle under the basis ⁇
  • the sending terminal performs (GH) -1 measurement and (GCNOT) -1 operation on the particles held by it, and keeps the information to be transmitted in the sending terminal.
  • the present invention also provides a high-dimensional multi-hop lossless teleportation method in which the transmitting terminal performs channel modulation right transfer, including:
  • the sending terminal and the receiving terminal are connected through several intermediate nodes, any one of the several intermediate nodes having high-dimensional modulation capability is used as a modulating node, and the GHZ between the sending terminal and the modulating node is determined channel;
  • the information to be transmitted is sent from the sending terminal to the receiving terminal, and at the same time, the modulation node introduces auxiliary particles to perform unitary operation to modulate the channel, and when the channel modulation is successful, the sending terminal, the modulation node and the intermediate The node performs a measurement operation, sends the measurement result to the receiving terminal, and the receiving terminal performs unitary transformation to recover the information to be transmitted. If the channel modulation fails, the transmitting terminal recovers the information to be transmitted.
  • the present invention also provides a high-dimensional multi-hop lossless teleportation method in which the modulation node performs channel modulation right transfer, including:
  • the information to be transmitted is determined by the The sending terminal sends to the receiving terminal;
  • the modulation node introduces auxiliary particles to perform unitary operations to modulate the channel. If the channel modulation is successful, the modulation node performs a measurement operation, and sends the measurement results and the measurement results of the sending terminal and the intermediate node to the receiving terminal and The receiving terminal performs unitary transformation to restore the information to be transmitted, and if the channel modulation fails, the sending terminal restores the information to be transmitted.
  • the present invention is used to form a direct d-dimensional entanglement channel shared between the sending terminal and the receiving terminal through parallel entanglement exchange, which can retain the original unknown state information transmitted in the case of teleportation failure, reducing the transmission terminal and The technical requirements of the receiving terminal.
  • FIG. 1 is a schematic flowchart of a high-dimensional multi-hop lossless teleportation method for channel modulation right transfer according to the present invention.
  • Fig. 2 is a quantum circuit diagram of the direct entanglement channel state formed based on the high-dimensional non-maximally entangled GHZ channel of the present invention.
  • Fig. 3 is a quantum circuit diagram of the lossless teleportation based on the high-dimensional direct entanglement GHZ channel of the present invention.
  • Fig. 4 is an example of a specific lossless teleportation quantum circuit diagram of the present invention.
  • a high-dimensional multi-hop lossless teleportation method for channel modulation right transfer of the present invention includes the following steps:
  • Step S100 Use any intermediate node with high-dimensional modulation capability among several intermediate nodes as a modulating node, and determine the GHZ channel between the transmitting terminal and the modulating node and the channel between the modulating node and the receiving terminal between GHZ channels.
  • the directly entangled GHZ state is usually not shared between the sending terminal and the receiving terminal, and the two communication terminals are connected through multiple intermediate nodes.
  • the current research results are difficult to support the accurate realization of double-qubit operations, quantum unitary transformations, high-dimensional multi-particle quantum operations, etc. in different physical systems. Therefore, it is necessary to equip multiple communication nodes in the network with quantum high-dimensional operation devices. Unrealistic.
  • the intermediate node Relayk with high-dimensional quantum operation capability is defined as a modulation node, and the modulation node is used for channel modulation, and the rest of the intermediate nodes are ordinary nodes, which only have simple quantum processing capabilities, such as a single Particle measurement and Bell measurement, etc., which greatly enhance the flexibility and practicability of the network.
  • Step S200 The information to be transmitted is sent from the sending terminal to the receiving terminal.
  • Step S300 The modulation node introduces auxiliary particles to perform unitary operation to modulate the channel. If the channel modulation is successful, the transmitting terminal, the modulating node and the intermediate node perform a measurement operation, and send the measurement result to the receiving In the terminal, the receiving terminal performs unitary transformation to restore the information to be transmitted, and if the channel modulation fails, the sending terminal restores the information to be transmitted.
  • the sending terminal Alice holds an unknown single-bit quantum state t and A 1
  • the receiving terminal Bob holds the target particle C N+1
  • Other intermediate nodes are divided into upstream nodes and downstream nodes with Relayk as the boundary.
  • the intermediate node between the sending terminal Alice and Relay k is called the upstream node
  • the intermediate node between the receiving terminal Bob and Relay k is called the downstream node.
  • N+1 non-maximally entangled GHZ channels can be expressed as
  • K-1 upstream nodes and N-(K+1) downstream nodes are simultaneously performing high-dimensional Bell measurements on their own particles C i A i+1 , and performing high-dimensional GH measurements on particles B i , And send the measurement result to node Alice and Relay k .
  • the upstream node as an example, the original quantum state of particles A 1 B 1 C 1 ...A k B k C k can be expressed as
  • Relay k Similar to establishing the upstream entanglement channel of particles A 1 , B k and C k , according to the generalized Bell measurement results and GH measurement results of all downstream nodes, Relay k performs the following unitary operation on its particle A k+1 , and Relay k and the direct entanglement channel of information receiving terminal Bob,
  • the direct entanglement channel between Relay k and Bob can be obtained after performing the unitary operation on particle A k+1 .
  • the states of the remaining particles A k+1 , B N+1 and C N+1 can be expressed as:
  • the multi-hop teleportation system has been simplified into a three-hop entanglement system composed of Alice, Relay k , Relay N+1 and Bob.
  • Relay k introduces an auxiliary particle e whose initial state is
  • the teleportation process is divided into the following three operational steps:
  • Step 1 Alice executes the GCNOT operation on her two particles t and A1, and then executes the GH operation on her first particle t, the whole system state becomes:
  • Step 2 While step 1 is being executed, Relay k performs the following unitary operations on the three particles C k , A k+1 and e held:
  • Relayk performs single-bit state measurement on the auxiliary particle e under the basis ⁇
  • Step 3 Assuming that the measurement result of Relay k is
  • Step 3' If the measurement result of particle e is
  • the quantum teleportation fails.
  • Alice performs a (GH) -1 on the particle t, and then executes (GCNOT on the two particles t and A1 ) -1 operation. After performing these two operations, the quantum state becomes:
  • Fig. 4 Please refer to Fig. 4, the following describes in detail a high-dimensional multi-hop lossless teleportation method for channel modulation right transfer of the present invention in the form of an embodiment.
  • the embodiment takes the sending terminal Alice, the receiving terminal Bob and three intermediate nodes as examples , so that the sending terminal Alice transmits unknown quantum state information to the receiving terminal Bob.
  • the sending terminal Alice holds particles t and A 1
  • the receiving terminal Bob holds particle C 4
  • the intermediate node Relay 2 has complex quantum computing capabilities, and it performs high-dimensional quantum unitary operations as a modulation node
  • Relay 1 and Relay 3 serve as Ordinary intermediate nodes assist in establishing quantum channels.
  • the sending terminal Alice holds an unknown single-bit quantum state t and A 1
  • the receiving terminal Bob holds the target particle C 4
  • the boundary is divided into upstream nodes and downstream nodes.
  • the intermediate node between the sending terminal Alice and the modulating node Relay 2 is called an upstream node
  • the intermediate node between the modulating node Relay 2 and the receiving terminal Bob is called a downstream node.
  • the source particle t held by the sending terminal Alice has the following unknown quantum state:
  • the channel parameters of each channel satisfy the normalization condition.
  • both the upstream node Relay 1 and the downstream node Relay 3 hold the two particles C 1 A 2 and C 3 A 4 basis Under the generalized Bell measurement, at the same time, the upstream node Relay 1 and the downstream node Relay 3 are in the base Next, conduct GH measurements on the particles B 1 and B 3 they hold, and they send the measurement results to the modulation node Relay 2 .
  • Relay 2 performs the following unitary operations to establish the upstream direct entanglement channel and the downstream direct entanglement channel respectively:
  • a 0 a 11 a 20
  • a 1 a 12 a 21
  • a 2 a 10 a 22 ,
  • Relay 2 performs high-dimensional unitary operations on the three particles C 2 , A 3 and e held in the formula
  • the collapsed state of Relay 2 after performing channel modulation is:
  • Relay 2 performs single-bit state measurement on the auxiliary particle e under the basis ⁇
  • the embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.
  • computer-usable storage media including but not limited to disk storage, CD-ROM, optical storage, etc.
  • These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to operate in a specific manner, such that the instructions stored in the computer-readable memory produce an article of manufacture comprising instruction means, the instructions
  • the device realizes the function specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

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Abstract

本发明公开了一种信道调制权转移的高维多跳无损隐形传送方法，包括将若干中间节点中的任意一个具有高维调制能力的中间节点作为调制节点，并确定发送终端与调制节点之间的GHZ信道以及调制节点与接收终端之间的GHZ信道；待传送信息由发送终端发送至接收终端；由调制节点引入辅助粒子进行幺正操作对信道进行调制，若信道调制成功，则由发送终端、调制节点以及中间节点进行测量操作，并将测量结果发送给接收终端，由接收终端执行幺正变换恢复出待传送信息，若信道调制失败，则由发送终端将待传送信息保留。本发明将复杂的高维信道调制操作转交给调制节点，同时引入辅助粒子来执行复杂的高维量子操作，通过各个通信节点协同合作完成信息传送。

Description

信道调制权转移的高维多跳无损隐形传送方法 技术领域
本发明涉及通信网络及信息传播技术领域，尤其涉及信道调制权转移的高维多跳无损隐形传送方法。
背景技术
目前量子通信理论包含三个主要分支：量子秘钥分发(Quantum Key Distribution,QKD)、量子安全直接通信(Quantum Secure Direct Communication,QSDC)以及量子隐形传态(Quantum Teleportation,QT)。其中量子安全直接通信的目的是借助量子信道在通信者之间传输经典消息，与之相对应的是在通信者之间直接传输量子态。早在1993年Bennett等学者首次提出量子隐形传态的概念，即通信双方共享纠缠对，发送终端不需要发送粒子本身就能将未知量子态传送到远端的另一个粒子上。特别是1997年底奥地利Zeilinger研究小组首先在实验上成功的演示量子隐形传态，此后，这一新兴理论迅速成为量子通信领域的一个研究热点，各种各样的隐形传态方法以及实验也被相继提出。
量子隐形传态在量子通信和量子信息中起着重要作用，它代表了许多量子技术发展的基本要素，例如量子中继器、量子门隐形传态、基于测量的计算以及端口-基于量子隐形传态等。其中量子隐形传态的过程如下：首先，发送者Alice和接收者Bob共享一个最大纠缠的贝尔信道；然后，Alice以Bell为基础对她的两个粒子执行联合测量，并将结果告知Bob；之后根据测量结果，Bob对其粒子执行四个幺正操作之一以恢复原始信息。如果Alice能够区分所有四种可能的测量结果，则原则上可以以100％的成功率完成传送过程，这称为确定性传送。确定性量子隐形传态通常依赖于最大纠缠信道。然而，在现实的隐形传送场景中，由于量子态与其周围环境之间不可避免的耦合效应，大多数信道很容易从最大纠缠态演变为非最大纠缠态。这将增加信息丢失的风险并降低信道的保真度。之后，若干概率隐形传态方案被提出，它们利用各种非最大纠缠态作为量子信道，如爱因斯坦-波多尔斯基-罗森(EPR)状态、团簇状态，W状态以及混合状态等。如Li等人提出了一种概率隐形传态方案，以多种非最大纠缠的贝尔态作为量子信道来传输未知的量子态。Chen等人提出了一个概率的隐形传态协议，该协议具有多个部分纠缠的贝尔状态，以传送未知的多粒子GHZ状态。高等人提出了一种方案，用两个三粒子纠缠的W态作为量子信道来传送未知的三粒子W态。
众所周知，在d维量子系统中执行幺正运算比在二维中执行更具挑战性。近些年来，d维量子系统中的一些隐形传态协议已经被提出了。例如，Wei等人报 告了多方共享d维隐形传态协议。周等人给出了任意d维m粒子的受控隐形传态的一般形式。Long等人提出了一种传输任意d维GHZ状态的方案。据我们所知，还没有关于所有参与的节点都通过网络中不同的d维GHZ信道进行链接的非破坏性隐形传送方案的报告。注意到余下的挑战是当概率隐形传态失败时如何保留原始未知状态。为了实现具有多个部分纠缠信道的确定性隐形传态，研究人员引入了辅助粒子来辅助未知的粒子状态传输。例如，Roa等人提出了一种方案，当概率远传失败时，发送终端仍可以恢复原始的未知状态。后来，付等人报道了一种多跳无损传送协议，该协议使用多个非最大纠缠的贝尔对作为信道。
但是目前缺少解决量子通信网络中最大纠缠信道非最大纠缠演化问题以及高维多粒子幺正操作难以执行问题的隐形传态方法。
发明内容
为此，本发明所要解决的技术问题在于克服现有技术中缺少解决量子通信网络中最大纠缠信道非最大纠缠演化问题以及高维多粒子幺正操作难以执行问题的隐形传态方法的问题。
为了解决上述的技术问题，本发明提供了一种由系统实现信道调制权转移的高维多跳无损隐形传送方法，所述系统包括发送终端、接收终端和若干中间节点，方法包括：
将若干中间节点中的任意一个具有高维调制能力的中间节点作为调制节点，并确定所述发送终端与所述调制节点之间的GHZ信道以及所述调制节点与所述接收终端之间的GHZ信道；
待传送信息由所述发送终端发送至所述接收终端；
由所述调制节点引入辅助粒子进行幺正操作对信道进行调制，若信道调制成功，则由所述发送终端、调制节点以及中间节点进行测量操作，并将测量结果发送给所述接收终端，由所述接收终端执行幺正变换恢复出待传送信息，若信道调制失败，则由所述发送终端恢复出待传送信息。
在本发明的一个实施例中，确定所述发送终端与所述调制节点之间的GHZ信道，包括：
由所述发送终端和所述调制节点之间的中间节点执行广义Bell态测量和GH测量，并将测量结果发送至发送终端，由所述发送终端执行幺正操作来构建所述发送终端与所述调制节点之间的GHZ信道。
在本发明的一个实施例中，确定所述调制节点与所述接收终端之间的GHZ信道，包括：
由所述调制节点和所述接收终端之间的中间节点执行广义Bell态测量和GH测量，并将测量结果发送至调制节点，并由所述调制节点执行幺正操作来构建所述调制节点与所述接收终端之间的GHZ信道。
在本发明的一个实施例中，连接所述发送终端、调制节点以及接收终端之间的两个非最大纠缠态如下：
Figure PCTCN2022078320-appb-000001
Figure PCTCN2022078320-appb-000002
式中，
Figure PCTCN2022078320-appb-000003
是信道参数且满足归一化条件
Figure PCTCN2022078320-appb-000004
在本发明的一个实施例中，待传送信息由所述发送终端发送至所述接收终端的同时，由所述调制节点进行幺正操作进行信道调制，包括：
由所述发送终端对其持有的粒子进行Bell测量，并对所述调制节点与所述中间节点持有的粒子进行GH操作，同时，所述调制节点对其持有的粒子进行幺正操作进行信道调制，其中所述调制节点持有的粒子包括引入的辅助粒子。
在本发明的一个实施例中，由所述调制节点引入辅助粒子进行幺正操作对信道进行调制，包括：
所述调制节点在基{|0>,|1>}下对辅助粒子进行测量操作，若所述调制节点的测量结果为|0> e，则由所述发送终端、调制节点以及中间节点进行测量操作，并将测量结果发送给所述接收终端，由所述接收终端执行幺正变换恢复出待传送信息；若所述调制节点的测量结果为|1> e，则由所述发送终端将所述待传送信息保留在所述发送终端。
在本发明的一个实施例中，所述调制节点在基{|0>,|1>}下对辅助粒子进行测量操作，若所述调制节点的测量结果为|0> e，则由所述发送终端、调制节点以及中间节点进行测量操作，并将测量结果发送给所述接收终端，由所述接收终端执行幺正变换恢复出待传送信息，包括：
由所述发送终端对其持有的粒子进行正交投影测量，得到第一测量结果；
由所述调制节点和中间节点分别对其持有的粒子进行GH测量，同时，所述调制节点对其持有的粒子进行Bell测量，得到第二测量结果；
将所述第一测量结果和所述第二测量结果发送至所述接收终端，由所述接收终端执行幺正变换恢复出待传送信息。
在本发明的一个实施例中，所述调制节点在基{|0>,|1>}下对辅助粒子进行测量操作，若所述调制节点的测量结果为|1> e，则由所述发送终端将所述待传送信息保留在所述发送终端，包括：
由所述发送终端对其持有的粒子进行(GH) -1测量和(GCNOT) -1操作，将所述待传送信息保留在所述发送终端。
此外，本发明还提供一种由发送终端执行信道调制权转移的高维多跳无损隐形传送方法，包括：
所述发送终端与接收终端之间通过若干中间节点连接，将若干中间节点中的任意一个具有高维调制能力的中间节点作为调制节点，并确定所述发送终端与所述调制节点之间的GHZ信道；
待传送信息由所述发送终端发送至所述接收终端，同时由所述调制节点引入辅助粒子进行幺正操作对信道进行调制，并在信道调制成功时，由所述发送 终端、调制节点以及中间节点进行测量操作，将测量结果发送给所述接收终端并由所述接收终端执行幺正变换恢复出待传送信息，若信道调制失败，则由所述发送终端恢复出待传送信息。
并且，本发明还提供一种由调制节点执行信道调制权转移的高维多跳无损隐形传送方法，包括：
将发送终端与接收终端之间的若干中间节点中的任意一个具有高维调制能力的中间节点作为调制节点，并确定所述调制节点与所述接收终端之间的GHZ信道，待传送信息由所述发送终端发送至所述接收终端；
所述调制节点引入辅助粒子进行幺正操作对信道进行调制，若信道调制成功，则由所述调制节点进行测量操作，将测量结果与发送终端及中间节点的测量结果发送给所述接收终端并由所述接收终端执行幺正变换恢复出待传送信息，若信道调制失败，则由所述发送终端恢复出待传送信息。
本发明的上述技术方案相比现有技术具有以下优点：
1、本发明发送终端与接收终端之间没有直接共享的纠缠态，需要借助于若干中间节点的帮助，将复杂的高维信道调制操作转交给具有高信息处理能力的调制节点，同时引入辅助粒子来执行复杂的高维量子操作通过各个通信节点协同合作完成信息传送。
2、本发明通过并行纠缠交换用于形成在发送终端和接收终端之间共享的直接d维纠缠信道，它能够在隐形传态失败的情况下保留传送的原始未知态信息，降低了发送终端和接收终端的技术要求。
附图说明
为了使本发明的内容更容易被清楚的理解，下面根据本发明的具体实施例并结合附图，对本发明作进一步详细的说明。
图1为本发明的一种信道调制权转移的高维多跳无损隐形传送方法的流程示意图。
图2为本发明的基于高维非最大纠缠GHZ信道形成直接纠缠信道态量子线路图。
图3为本发明的基于高维直接纠缠GHZ信道的无损隐形传态的量子线路图。
图4为本发明的具体无损隐形传送量子线路图实例。
具体实施方式
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。
请参阅图1所示，本发明一种信道调制权转移的高维多跳无损隐形传送方法包括如下步骤：
步骤S100：将若干中间节点中的任意一个具有高维调制能力的中间节点作为调制节点，并确定所述发送终端与所述调制节点之间的GHZ信道以及所述 调制节点与所述接收终端之间的GHZ信道。
示例地，在现实的隐形传送过程中，发送终端和接收终端之间通常不会共享直接纠缠的GHZ状态，两个通信终端之间通过多个中间节点连接。然而目前的研究成果难以支持在不同的物理系统中准确地实现双量子比特操作、量子幺正变换、高维多粒子量子运算等，因此为网络中的多个通信节点配备量子高维操作设备是不现实的。因此本发明在所有中间节点中，将具有高维量子操作能力的中间节点Relayk定义为调制节点，利用调制节点进行信道调制，其余的中间节点是普通节点，只具有简单的量子处理能力，如单粒子测量和Bell测量等，这样便极大地增强网络的灵活性与实用性。
步骤S200：待传送信息由所述发送终端发送至所述接收终端。
步骤S300：由所述调制节点引入辅助粒子进行幺正操作对信道进行调制，若信道调制成功，则由所述发送终端、调制节点以及中间节点进行测量操作，并将测量结果发送给所述接收终端，由所述接收终端执行幺正变换恢复出待传送信息，若信道调制失败，则由所述发送终端恢复出待传送消息。
综上，本发明发送终端与接收终端之间没有直接共享的纠缠态，需要借助于若干中间节点的帮助，将复杂的高维信道调制操作转交给具有高信息处理能力的调制节点，同时引入辅助粒子来执行复杂的高维量子操作通过各个通信节点协同合作完成信息传送。
具体的，请参阅图2和图3所示，发送终端Alice持有一个未知单比特量子态t和A 1，接收终端Bob持有目标粒子C N+1，通信双方通过N个中间节点Relay q(q＝1,2,…,N)间接相连。由于不可能为每个通信节点都提供复杂的量子运算能力，因此考虑让具有高维多qudits量子操作能力的中间节点Relay k执行高维量子幺正操作。其他中间节点以Relayk为界划分为上游节点和下游节点。发送终端Alice和Relay k之间的中间节点称为上游节点，接收终端Bob和Relay k之间的中间节点则称为下游节点。
其中N+1个非最大纠缠GHZ信道可以表示为
Figure PCTCN2022078320-appb-000005
式中
Figure PCTCN2022078320-appb-000006
表示信道参数并且满足归一化条件
Figure PCTCN2022078320-appb-000007
第一个下标q(q＝1,2,…,N+1)表示纠缠信道序号。
首先，K-1个上游节点和N-(K+1)下游节点同时对自己所持有的粒子C iA i+1在执行高维Bell测量，并且对粒子B i执行高维GH测量，并将测量结果发送给节点Alice和Relay k。以上游节点为例，由粒子A 1B 1C 1…A kB kC k原始量子态可以表示为
Figure PCTCN2022078320-appb-000008
初始约束条件为l k＝0。值得注意的是，累乘项
Figure PCTCN2022078320-appb-000009
表示约束条件(l q-1+j)mod d＝(l q-n q-1)mod d(q＝k-1,k-2,…,1；j＝0,1,…,d-1)限制下的纠缠信道参数。其中
Figure PCTCN2022078320-appb-000010
和
Figure PCTCN2022078320-appb-000011
为了在通信方与Relay k形成直接纠缠GHZ信道，所有中间节点Relay q(q＝1,2,…,k-1)在
Figure PCTCN2022078320-appb-000012
的基础上同时对自己的粒子C i和A i+1执行广义Bell态测量。将d2种可能的测量结果发送给Alice。根据测量结果Alice执行下列幺正操作来调制上游纠缠信道：
Figure PCTCN2022078320-appb-000013
其中
Figure PCTCN2022078320-appb-000014
如果忽略全局因子，则剩余粒子A 1，B k和C k的状态变为：
Figure PCTCN2022078320-appb-000015
为了简化方程式，我们假设
Figure PCTCN2022078320-appb-000016
最后直接纠缠状态可以重写为：
Figure PCTCN2022078320-appb-000017
与建立粒子A 1,B k和C k的上游纠缠信道相似，根据所有下游节点的广义Bell测量结果和GH测量结果，Relay k对其粒子A k+1执行如下幺正操作，即可得Relay k和信息接收终端Bob的直接纠缠信道，
Figure PCTCN2022078320-appb-000018
在粒子A k+1执行完幺正操作即可得到Relay k与Bob之间的直接纠缠信道。剩余粒子A k+1，B N+1和C N+1的状态可以表示为：
Figure PCTCN2022078320-appb-000019
经过上述操作，多跳隐形传态系统已经简化为由Alice、Relay k，Relay N+1和Bob构成的三跳纠缠系统。
假设Alice想要传送如下的未知量子t给Bob
Figure PCTCN2022078320-appb-000020
式中，c j(j＝0,1,…,d-1)是复数，并且满足归一化条件
Figure PCTCN2022078320-appb-000021
连接通信三方的两个非最大纠缠态如下：
Figure PCTCN2022078320-appb-000022
Figure PCTCN2022078320-appb-000023
上面两个式子中，
Figure PCTCN2022078320-appb-000024
是信道参数且满足归一化条件
Figure PCTCN2022078320-appb-000025
Alice持有粒子t和A 1。Relay k引入一个初始态为|0> e的辅助粒子e，持有粒子B kC kA k+1和e，Relay N+1持有粒子B N+1和目标节点，Bob拥有粒子C N+1。则粒子t,A 1,B k,C k,A k+1,B N+1,C N+1以及e的系统态为
Figure PCTCN2022078320-appb-000026
准备好信道后，隐形传态过程分为以下三个操作步骤：
步骤1：Alice对她持有的两个粒子t和A1执行GCNOT操作，然后对其第一个粒子t执行GH操作，整个系统态变为：
Figure PCTCN2022078320-appb-000027
与此同时还需要对粒子B k和B N+1执行GH操作，则整个系统变为：
Figure PCTCN2022078320-appb-000028
步骤2：在步骤1执行的同时，Relay k对持有的三个粒子C k,A k+1和e进行如下幺正操作：
Figure PCTCN2022078320-appb-000029
式中
Figure PCTCN2022078320-appb-000030
Relayk执行完信道调制后的粒子状态变为如下 形式：
Figure PCTCN2022078320-appb-000031
然后，Relayk在基{|0>,|1>}下对辅助粒子e执行单比特态测量，可得到|0> e或|1> e，若Relay k的测量结果为|0> e，则接下来执行步骤3恢复原始未知量子态；否则执行步骤3’将传送的粒子态保留在发送终端位置。
步骤3：假设Relay k的测量结果为|0> e，则剩余粒子的坍缩态为：
Figure PCTCN2022078320-appb-000032
接下来，Alice在标准基{|rs>}(r,s＝0,1,2,…,d-1)下对其持有的两个粒子t和A 1进行正交投影测量，Relay k和Relay N+1在基
Figure PCTCN2022078320-appb-000033
的作用下对所持有粒子B k和B N+1进行GH测量。同时Relay k在正交基
Figure PCTCN2022078320-appb-000034
下对粒子C k和A k+1进行Bell测量。测量操作之后，Alice，Relay k和Relay N+1分别将测量结果发送给接收终端Bob，根据测量结果
Figure PCTCN2022078320-appb-000035
和
Figure PCTCN2022078320-appb-000036
Bob执行相应的幺正变换来恢复传送的未知量子态。幺正变换如式所示：
Figure PCTCN2022078320-appb-000037
当Bob执行相应的幺正变换，信息传送已经完成，恢复的未知量子态为：
Figure PCTCN2022078320-appb-000038
步骤3’如果对粒子e的测量结果为|1> e，相应的坍缩态为：
Figure PCTCN2022078320-appb-000039
此时量子隐形传态失败，为保留原始的量子态信息以便通过其他可用的量 子信道进行信息重传，Alice对粒子t执行一个(GH) -1，然后对两个粒子t和A1执行(GCNOT) -1操作。执行完这两项操作之后，量子态变为：
Figure PCTCN2022078320-appb-000040
其中
Figure PCTCN2022078320-appb-000041
和GCNOT -1|mn>＝|m>|(n-m)mod d>。可以发现，粒子t的态不变，因此原始未知量子态被保存下来。
请参阅图4所示，下面以实施例的方式详细介绍本发明一种信道调制权转移的高维多跳无损隐形传送方法，实施例以发送终端Alice、接收终端Bob和3个中间节点为例，实现发送终端Alice向接收终端Bob传送未知量子态信息。
其中发送终端Alice持有粒子t和A 1，接收终端Bob持有粒子C 4，中间节点Relay 2具有复杂量子运算能力，其作为调制节点执行高维量子幺正操作，同时Relay 1和Relay 3作为普通的中间节点协助建立量子信道。
发送终端Alice持有一个未知单比特量子态t和A 1，接收终端Bob持有目标粒子C 4，通信双方通过3个中间节点Relay q(q＝1,2,3)间接相连，以Relay 2为界划分为上游节点和下游节点。发送终端Alice与调制节点Relay 2之间的中间节点称为上游节点，调制节点Relay 2和接收终端Bob之间的中间节点则称为下游节点。
发送终端Alice持有的信源粒子t具有如下未知量子态：
|χ> t＝c 0|0>+c 1|1>+c 2|2>,
式中|c 0| 2+|c 1| 2+|c 2| 2＝1。各相邻节点间的非最大纠缠GHZ态为：
Figure PCTCN2022078320-appb-000042
Figure PCTCN2022078320-appb-000043
Figure PCTCN2022078320-appb-000044
Figure PCTCN2022078320-appb-000045
其中每个信道的信道参数满足归一化条件。
首先，上游节点Relay 1和下游节点Relay 3都对其持有的两个粒子C 1A 2和C 3A 4基
Figure PCTCN2022078320-appb-000046
下执行广义Bell测量，同时，上游节点Relay 1和下游节点Relay 3在基
Figure PCTCN2022078320-appb-000047
下对其持有的粒子B 1和B 3进行GH测量，他们将测量结果发送给调制节点Relay 2。
假设Relay 1和Relay 3的坍塌态为
Figure PCTCN2022078320-appb-000048
和
Figure PCTCN2022078320-appb-000049
则粒子对C 1A 2和C 3A 4的测量结果为
Figure PCTCN2022078320-appb-000050
和
Figure PCTCN2022078320-appb-000051
的对应关系,以及粒子
Figure PCTCN2022078320-appb-000052
和
Figure PCTCN2022078320-appb-000053
的坍缩态与测量结果
Figure PCTCN2022078320-appb-000054
和
Figure PCTCN2022078320-appb-000055
的对应关系如下表所示：
Figure PCTCN2022078320-appb-000056
为便于分析，进一步假设粒子C 1A 2和C 3A 4的广义Bell测量结果为
Figure PCTCN2022078320-appb-000057
粒子B 1和B 3的广义Bell测量结果为
Figure PCTCN2022078320-appb-000058
Figure PCTCN2022078320-appb-000059
则粒子对C 1A 2和C 3A 4以及粒子B 2和B 4的坍缩态为:
Figure PCTCN2022078320-appb-000060
Figure PCTCN2022078320-appb-000061
Figure PCTCN2022078320-appb-000062
Figure PCTCN2022078320-appb-000063
则坍缩态
Figure PCTCN2022078320-appb-000064
和
Figure PCTCN2022078320-appb-000065
就可以写为：
Figure PCTCN2022078320-appb-000066
Figure PCTCN2022078320-appb-000067
Relay 2执行如下幺正操作来分别建立上游直接纠缠信道以及下游直接纠缠信道：
Figure PCTCN2022078320-appb-000068
Figure PCTCN2022078320-appb-000069
执行幺正操作之后，则坍缩态
Figure PCTCN2022078320-appb-000070
和
Figure PCTCN2022078320-appb-000071
就可以写为：
Figure PCTCN2022078320-appb-000072
Figure PCTCN2022078320-appb-000073
为简化公式表达，两个纠缠信道参数分别写作：
a 0＝a 11a 20,a 1＝a 12a 21,a 2＝a 10a 22,
b 0＝a 32a 40,b 1＝a 30a 41,b 2＝a 31a 42.
接着Alice对她持有的两个粒子t和A 1执行GCNOT操作，然后对其第一个粒子t执行GH操作，与此同时还需要对粒子B 2和B 4执行GH操作，则整个系统变为：
Figure PCTCN2022078320-appb-000074
接着，Relay 2对持有的三个粒子C 2,A 3和e进行高维幺正操作式中
Figure PCTCN2022078320-appb-000075
Relay 2执行完信道调制后的坍缩态为：
Figure PCTCN2022078320-appb-000076
然后，Relay 2在基{|0>,|1>}下对辅助粒子e执行单比特态测量，可得到|0> e或|1> e，假设辅助粒子的测量结果为|0> e，则剩余粒子的坍缩态为：
Figure PCTCN2022078320-appb-000077
接下来，Alice在标准基{|rs>}(r,s＝0,1,2)下对其持有的两个粒子t和A 1进行正交投影测量，Relay 2和Relay 4在基
Figure PCTCN2022078320-appb-000078
的作用下对所持有粒子B 2和B 4进行GH测量。同时Relay 2在正交基
Figure PCTCN2022078320-appb-000079
下对粒子C 2和A 3进行Bell测量。测量操作之后，Alice，Relay 2和Relay 4分别将测量结果发送 给接收终端Bob，假设测量结果为
Figure PCTCN2022078320-appb-000080
和
Figure PCTCN2022078320-appb-000081
粒子C 4的量子态相应坍缩为：
Figure PCTCN2022078320-appb-000082
Bob执行相应的幺正变换来恢复传送的未知量子态，其中幺正变换为：
Figure PCTCN2022078320-appb-000083
显然等式成立。因此当Bob执行相应的幺正变换，信息传送就会成功，恢复的未知量子态为：
Figure PCTCN2022078320-appb-000084
本领域内的技术人员应明白，本申请的实施例可提供为方法、系统、或计算机程序产品。因此，本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且，本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。
本申请是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器，使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。
这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中，使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品，该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。
这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上，使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理，从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。
显然，上述实施例仅仅是为清楚地说明所作的举例，并非对实施方式的限定。对于所属领域的普通技术人员来说，在上述说明的基础上还可以做出其它不同形式变化或变动。这里无需也无法对所有的实施方式予以穷举。而由此所引申出的显而易见的变化或变动仍处于本发明创造的保护范围之中。

Claims (10)

  1. 一种由系统实现信道调制权转移的高维多跳无损隐形传送方法，其特征在于，所述系统包括发送终端、接收终端和若干中间节点，方法包括：
    将若干中间节点中的任意一个具有高维调制能力的中间节点作为调制节点，并确定所述发送终端与所述调制节点之间的GHZ信道以及所述调制节点与所述接收终端之间的GHZ信道；
    待传送信息由所述发送终端发送至所述接收终端；
    由所述调制节点引入辅助粒子进行幺正操作对信道进行调制，若信道调制成功，则由所述发送终端、调制节点以及中间节点进行测量操作，并将测量结果发送给所述接收终端，由所述接收终端执行幺正变换恢复出待传送信息，若信道调制失败，则由所述发送终端恢复出待传送信息。
  2. 如权利要求1所述的由系统实现信道调制权转移的高维多跳无损隐形传送方法，其特征在于：确定所述发送终端与所述调制节点之间的GHZ信道，包括：
    由所述发送终端和所述调制节点之间的中间节点执行广义Bell态测量和GH测量，并将测量结果发送至发送终端，由所述发送终端执行幺正操作来构建所述发送终端与所述调制节点之间的GHZ信道。
  3. 如权利要求1所述的由系统实现信道调制权转移的高维多跳无损隐形传送方法，其特征在于：确定所述调制节点与所述接收终端之间的GHZ信道，包括：
    由所述调制节点和所述接收终端之间的中间节点执行广义Bell态测量和GH测量，并将测量结果发送至调制节点，并由所述调制节点执行幺正操作来构建所述调制节点与所述接收终端之间的GHZ信道。
  4. 如权利要求1所述的由系统实现信道调制权转移的高维多跳无损隐形传送方法，其特征在于：连接所述发送终端、调制节点以及接收终端之间的两个非最大纠缠态如下：
    Figure PCTCN2022078320-appb-100001
    Figure PCTCN2022078320-appb-100002
    式中，
    Figure PCTCN2022078320-appb-100003
    是信道参数且满足归一化条件
    Figure PCTCN2022078320-appb-100004
  5. 如权利要求1所述的由系统实现信道调制权转移的高维多跳无损隐形传送方法，其特征在于：待传送信息由所述发送终端发送至所述接收终端的同时，由所述调制节点进行幺正操作进行信道调制，包括：
    由所述发送终端对其持有的粒子进行Bell测量，并对所述调制节点与所述中间节点持有的粒子进行GH操作，同时，所述调制节点对其持有的粒子进行幺正操作进行信道调制，其中所述调制节点持有的粒子包括引入的辅助粒子。
  6. 如权利要求1所述的由系统实现信道调制权转移的高维多跳无损隐形传送方法，其特征在于：由所述调制节点引入辅助粒子进行幺正操作对信道进行 调制，包括：
    所述调制节点在基{|0>,|1>}下对辅助粒子进行测量操作，若所述调制节点的测量结果为|0> e，则由所述发送终端、调制节点以及中间节点进行测量操作，并将测量结果发送给所述接收终端，由所述接收终端执行幺正变换恢复出待传送信息；若所述调制节点的测量结果为|1> e，则由所述发送终端将所述待传送信息保留在所述发送终端。
  7. 如权利要求6所述的由系统实现信道调制权转移的高维多跳无损隐形传送方法，其特征在于：所述调制节点在基{|0>,|1>}下对辅助粒子进行测量操作，若所述调制节点的测量结果为|0> e，则由所述发送终端、调制节点以及中间节点进行测量操作，并将测量结果发送给所述接收终端，由所述接收终端执行幺正变换恢复出待传送信息，包括：
    由所述发送终端对其持有的粒子进行正交投影测量，得到第一测量结果；
    由所述调制节点和中间节点分别对其持有的粒子进行GH测量，同时，所述调制节点对其持有的粒子进行Bell测量，得到第二测量结果；
    将所述第一测量结果和所述第二测量结果发送至所述接收终端，由所述接收终端执行幺正变换恢复出待传送信息。
  8. 如权利要求6所述的由系统实现信道调制权转移的高维多跳无损隐形传送方法，其特征在于：所述调制节点在基{|0>,|1>}下对辅助粒子进行测量操作，若所述调制节点的测量结果为|1> e，则由所述发送终端将所述待传送信息保留在所述发送终端，包括：
    由所述发送终端对其持有的粒子进行(GH) -1测量和(GCNOT) -1操作，将所述待传送信息保留在所述发送终端。
  9. 一种由发送终端执行信道调制权转移的高维多跳无损隐形传送方法，其特征在于，包括：
    所述发送终端与接收终端之间通过若干中间节点连接，将若干中间节点中的任意一个具有高维调制能力的中间节点作为调制节点，并确定所述发送终端与所述调制节点之间的GHZ信道；
    待传送信息由所述发送终端发送至所述接收终端，同时由所述调制节点引入辅助粒子进行幺正操作对信道进行调制，并在信道调制成功时，由所述发送终端、调制节点以及中间节点进行测量操作，将测量结果发送给所述接收终端并由所述接收终端执行幺正变换恢复出待传送信息，若信道调制失败，则由所述发送终端恢复出待传送信息。
  10. 一种由调制节点执行信道调制权转移的高维多跳无损隐形传送方法，其特征在于，包括：
    将发送终端与接收终端之间的若干中间节点中的任意一个具有高维调制能力的中间节点作为调制节点，并确定所述调制节点与所述接收终端之间的GHZ信道，待传送信息由所述发送终端发送至所述接收终端；
    所述调制节点引入辅助粒子进行幺正操作对信道进行调制，若信道调制成功，则由所述调制节点进行测量操作，将测量结果与发送终端及中间节点的测 量结果发送给所述接收终端并由所述接收终端执行幺正变换恢复出待传送信息，若信道调制失败，则由所述发送终端恢复出待传送信息。
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