图态的远程制备及在量子密码协议中的应用
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摘要
图态是由多个部分组成且和数学图形相关的一类量子态,它的结构能通过数学图形以简洁且有效的方式来进行刻画。图态自提出以来一直是研究量子计算、量子纠错以及理解两体、多体纠缠结构的基础工具。除此之外,图态在量子密码技术中也有非常重要的应用。一些特殊的图态已经成为常见量子密码协议的基本资源,包括量子密钥分配、量子秘密共享和隐形传态等等。
本博士论文以图态为中心,主要研究图态的远程制备及图态在量子密码协议中的应用。
在图态的远程制备方面,把六粒子cluster态作为制备对象,利用GHZ态为量子信道设计了三种类型的远程制备协议,包括一般远程制备、联合远程制备和受控远程制备,并分析了方案成功的概率及所需的经典通信。方案中所用的资源在现有技术下均可实现,因此具有很好的可行性。
对于图态在量子密码中的应用,本文主要涉及了量子密码协议的两个分支,包括量子秘密共享协议和量子保密比较协议。
在量子秘密共享方面,针对应用中存在成员变更的实际问题,利用特殊的图态从理论角度提出了四个新的方案。第一个方案是基于线形cluster态设计的一方到三方量子信息分割方案。该方案具有除名能力,在秘密信息恢复前分发者能够删除任意一个参与者,并且在不需要重新分配量子份额的条件下与剩余的参与者共享新的量子秘密信息。在此方案基础上进一步研究,利用线形cluster态给出了具有除名能力的一方到n方量子信息秘密共享方案,分发者按照该方案最多可删除n-2个参与者。第三个方案和第四个方案是基于星形cluster态设计的能够添加和删除成员的秘密共享方案,分别考虑了共享信息为经典信息和量子信息的情况。与现有方案相比,本文的方案具有更好的灵活性和实用性,且在动态量子秘密共享研究中具有一定的开创性。
在量子保密比较方面,首先研究了χ类量子态在保密比较相等性问题中的应用,给出了一个新的量子保密比较协议。该协议利用纠缠交换和超密编码等量子技术,不仅保证了信息的机密性,还提高了比较的效率。另外,利用d级三粒子GHZ态首次以量子方式解决了保密比较大小问题,借助相对相位因子的特性有效地保证了数据的保密性和协议的公平性。
Graph states are quantum states of a system embodying several constituents, associated with a graph. Their structures can be described in a concise and fruitful way by mathematical graphs. They have been key instrumental tools in the development of models for quantum computing, of quantum error correction, and of grasping the structure of bi-and multi-partite entanglement. In addition to all these applications, graph states also play an important role in quantum cryptographic protocols. And some specific graph states are essential for several quantum communication protocols, including quantum key distribution, quantum secret sharing, teleportation and so on.
The contributions of this dissertation are mainly on the remote preparation and applications of graph states.
In our studies on the protocols related to remote state preparation (RSP), the remote preparations of a six-particle cluster state are consided with GHZ states as quantum channels, including common RSP, joint remote state preparation (JRSP) and controlled remote state preparation (CRSP). Moreover, the probability of success and classical communication costs in different cases are discussed. The resources and technologies used can be achieved, so the protocols are feasible.
The study on the applications of graph state involves two areas in quantum cryptographic protocols, including quantum secret sharing (QSS) and quantum private comparison (QPC).
In the field of QSS, four protocols on the problem of member changes in practice are developed based on different special graph states in theory. The first protocol is a one-to three-party quantum information splitting scheme with disenrollment capability. Before the reconstruction of the quantum information, the sender can delete any participant, and the remaining parties can share a new quantum key without setting a new quantum channel. Then it is generalized to the case of one-to n-party. In this protocol, the sender can delete n-2participants at most. The third and forth QSS protocols, which are based on star-cluster states, are discussed between a sender and a dynamic agent group for sharing classical and quantum information. Furthermore, these works are initiative in QSS, and they are more flexible and suitable for practical applications than existed schemes.
With respect to the field of QPC, two new theoretical protocols are proposed. χ-type states are used to determine the equality of two secret information based on quantum technologies such as entanglement swapping and dense coding. This protocol provides the privacy of information and a high efficiency. In addition, the first QPC protocol for solving the millionaire problem is designed based on d-level GHZ states. The essence of the relative phase factor can guarantee the confidentiality of the data and fairness of the protocol.
本博士论文以图态为中心,主要研究图态的远程制备及图态在量子密码协议中的应用。
在图态的远程制备方面,把六粒子cluster态作为制备对象,利用GHZ态为量子信道设计了三种类型的远程制备协议,包括一般远程制备、联合远程制备和受控远程制备,并分析了方案成功的概率及所需的经典通信。方案中所用的资源在现有技术下均可实现,因此具有很好的可行性。
对于图态在量子密码中的应用,本文主要涉及了量子密码协议的两个分支,包括量子秘密共享协议和量子保密比较协议。
在量子秘密共享方面,针对应用中存在成员变更的实际问题,利用特殊的图态从理论角度提出了四个新的方案。第一个方案是基于线形cluster态设计的一方到三方量子信息分割方案。该方案具有除名能力,在秘密信息恢复前分发者能够删除任意一个参与者,并且在不需要重新分配量子份额的条件下与剩余的参与者共享新的量子秘密信息。在此方案基础上进一步研究,利用线形cluster态给出了具有除名能力的一方到n方量子信息秘密共享方案,分发者按照该方案最多可删除n-2个参与者。第三个方案和第四个方案是基于星形cluster态设计的能够添加和删除成员的秘密共享方案,分别考虑了共享信息为经典信息和量子信息的情况。与现有方案相比,本文的方案具有更好的灵活性和实用性,且在动态量子秘密共享研究中具有一定的开创性。
在量子保密比较方面,首先研究了χ类量子态在保密比较相等性问题中的应用,给出了一个新的量子保密比较协议。该协议利用纠缠交换和超密编码等量子技术,不仅保证了信息的机密性,还提高了比较的效率。另外,利用d级三粒子GHZ态首次以量子方式解决了保密比较大小问题,借助相对相位因子的特性有效地保证了数据的保密性和协议的公平性。
Graph states are quantum states of a system embodying several constituents, associated with a graph. Their structures can be described in a concise and fruitful way by mathematical graphs. They have been key instrumental tools in the development of models for quantum computing, of quantum error correction, and of grasping the structure of bi-and multi-partite entanglement. In addition to all these applications, graph states also play an important role in quantum cryptographic protocols. And some specific graph states are essential for several quantum communication protocols, including quantum key distribution, quantum secret sharing, teleportation and so on.
The contributions of this dissertation are mainly on the remote preparation and applications of graph states.
In our studies on the protocols related to remote state preparation (RSP), the remote preparations of a six-particle cluster state are consided with GHZ states as quantum channels, including common RSP, joint remote state preparation (JRSP) and controlled remote state preparation (CRSP). Moreover, the probability of success and classical communication costs in different cases are discussed. The resources and technologies used can be achieved, so the protocols are feasible.
The study on the applications of graph state involves two areas in quantum cryptographic protocols, including quantum secret sharing (QSS) and quantum private comparison (QPC).
In the field of QSS, four protocols on the problem of member changes in practice are developed based on different special graph states in theory. The first protocol is a one-to three-party quantum information splitting scheme with disenrollment capability. Before the reconstruction of the quantum information, the sender can delete any participant, and the remaining parties can share a new quantum key without setting a new quantum channel. Then it is generalized to the case of one-to n-party. In this protocol, the sender can delete n-2participants at most. The third and forth QSS protocols, which are based on star-cluster states, are discussed between a sender and a dynamic agent group for sharing classical and quantum information. Furthermore, these works are initiative in QSS, and they are more flexible and suitable for practical applications than existed schemes.
With respect to the field of QPC, two new theoretical protocols are proposed. χ-type states are used to determine the equality of two secret information based on quantum technologies such as entanglement swapping and dense coding. This protocol provides the privacy of information and a high efficiency. In addition, the first QPC protocol for solving the millionaire problem is designed based on d-level GHZ states. The essence of the relative phase factor can guarantee the confidentiality of the data and fairness of the protocol.
引文
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