纠缠态的制备及其在量子通信中应用的理论研究
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摘要
量子信息学是二十世纪八十年代兴起的一门融合了量子力学和信息科学的新兴学科。近20年来,人们对量子信息学的研究,不论是理论上还是实验上都取得了长足的发展。作为量子信息学的核心部分,量子纠缠不仅是量子力学区别于经典力学的重要特征之一,也是量子信息理论的重要组成部分。作为量子理论最显著的特征之一,量子纠缠被当作一种有效的资源广泛地应用于量子信息领域。纠缠在量子信息处理中已经产生了许多有趣的应用,如量子隐形传态、量子密集编码、量子态远程制备、量子安全直接通信、量子秘密共享等等。所以,研究量子纠缠及其在量子信息中的应用,不仅对深刻理解量子力学的特性有着重要的学术意义,而且对开发和利用新型的信息处理方法等有着重要的实用价值。因此,本文主要在理论上研究了纠缠态的制备及其在量子通信中的应用(主要包括量子隐形传态、量子态远程制备、量子秘密共享和量子安全直接通信)。全文共分为七章,其中第三章到第七章是本人的工作,整篇论文内容的具体安排为:
第一章简要回顾了量子信息理论的提出和发展过程,简述了量子纠缠态的提出和定义,并在最后给出了本博士论文的主要研究内容和章节安排。
第二章主要介绍了量子信息的基本理论。首先介绍了EPR佯谬和Bell不等式,几类常见的纠缠态,量子纠缠态的度量,量子不可克隆定理以及几种主要的纠缠操作;然后介绍了几个典型的量子信息处理任务说明量子纠缠作为一个重要的物理资源在量子信息理论中的应用。
第三章主要讨论了利用线性光学元件制备多光子GHZ纠缠态。在这个方案中需要用到简单的线性光学元件,N对两光子极化纠缠态和常规光子探测器。因为实现本方案只需要在探测端口确认是否有光子,而不需要计数光子的数量,所以这就在一定程度上提高了实验上实现的可行性。
第四章主要讨论了量子纠缠态在量子隐形传送方面的应用。两个量子隐形传送方案被提出:第一个方案是利用一个非最大纠缠EPR对作为量子通道来传送N粒子非最大纠缠GHZ态。在这个方案中考虑了量子通道中存在振幅噪音的情况,这个方案可以被推广到传送任意能级N粒子非最大纠缠GHZ态的情况;第二个方案中考虑了利用一维四粒子非最大纠缠Cluster态作为量子通道传送一个任意未知的两比特纠缠态的情况。
第五章主要讨论了量子纠缠态在量子态远程制备中的应用。这一章中,不仅一对一的量子态远程制备的情况被考虑,而且多方联合远程制备量子纠缠态的情况也被考虑。
第六章主要讨论了量子纠缠态在量子秘密共享方面的应用。本章指出,不仅可以用非最大纠缠态作为量子通道实现多方量子秘密共享量子信息,而且利用线性光学的方法也可以实现量子秘密共享量子态。这两种方法的都有各自的优点和缺点。
第七章主要讨论了量子纠缠态在量子安全直接通信方面的应用。本章指出,利用非对称能级的纠缠态作为量子通道可以完美的实现受控量子安全直接通信。这个方案是安全的,高效的,每次信息传送量也大大提高了。而且这个方案可以推广到多方控制情况。
最后给出了全文的总结与展望。
The quantum informatics is an intersection of quantum mechanics and information theory, arisen from 1980s.Over the last two decades,there has been rapid development in both theoretical and experimental studies on quantum information.Quantum entanglement is not only one of the major characteristics that distinguish quantum from classical mechanics, but also an essential ingredient of quantum information theory.As one of the most striking features of quantum formalism,quantum entanglement is used in the field of quantum information as an effective resource.The entanglement has involved many interesting applications without classical counterparts,such as quantum teleportation,quantum dense coding,remote state preparation,quantum secure direct communication,and quantum secret sharing.Therefore,the study of both quantum entanglement and its applications in quantum information theory are necessary and valuable not only to understand well the special properties of the quantum mechanics but also to develop and make use of the new information process methods.Taking the problems stated above into account,theoretical study on preparation of entangled states and their applications in quantum communication are mainly discussed in this dissertation.The thesis has been divided into seven chapters,and our works are included in the chapters from 3 to 7.
In Chapter 1,the background of the study,the proposition and definition of quantum entanglement are introduced,and the major research subjects and the organization of the dissertation are given at the end of this chapter.
In Chapter 2,the basic conception of quantum information is introduced.Firstly,EPR paradox and Bell inequality,and several kinds of entangled states,as well as their properties, are given.Then the measurement of the degree of quantum entanglement,quantum nocloning theorem,and manipulation of quantum entanglement are introduced.At last,several typical quantum information protocols are also introduced in order to demonstrate that quantum entanglement is an important physical resource.
In Chapter 3,the protocol for generating Greenberger-Horne-Zeilinger(GHZ) state of N distant photons with linear optical elements is proposed.The proposed setup consist of simple linear optical elements,N pairs of the two-photon polarization entangled states,and the conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states.This makes the protocol more realizable in experiments.
In chapter 4,the applications of entangled states in quantum teleportation is discussed and two theoretical protocols are developed.In the first protocol,an arbitrary N-qubit GHZ entangled state can be probabilistically teleported from the sender to the receiver via only one non-maximally two qubit entangled state.Without entanglement concentration,using standard Bell-state measurement and classical communication one cannot teleport the state with unit fidelity and unit probability.In the second protocol,an arbitrary and unknown two-qubit entangled state can be probabilistically teleported from the sender to the receiver via a one-dimensional four-particle non-maximally entangled cluster state.By construction, the four-particle state is not reducible to a pair of Bell states.
In chapter 5,the applications of entangled states in remote state preparation is discussed and one theoretical protocol is proposed.In this protocol,one sender and one receiver case, and multiparty remote state preparation(That is two- or multi-party share a quantum state, and they want to remotely prepare it to the receiver) case are considered.
In chapter 6,the applications of entangled states in quantum secret sharing is discussed. A protocol is proposed for multiparty quantum secret sharing via introducing auxiliary particles using a non-maximally entangled two-particle state without a Bell measurement first, and then two optical protocols are proposed for quantum state sharing of superposed coherent states and entangled states,respectively.
In chapter 7,the applications of entangled states in quantum secret direct communication is discussed.A protocol is presented for controlled quantum secure direct communication that uses a 2-dimensional Greenberger-Horne-Zeilinger(GHZ) entangled state and a 3-dimensional Bell-basis state and employs the high-dimensional quantum superdense coding,local collective unitary operations and entanglement swapping.The proposed protocol is secure and of high source capacity.It can effectively protect the communication against a destroying-travelqubit -type attack.With this protocol,the information transmission is greatly increased. This protocol can also be modified,so that it can be used in a multi-party control system.
Finally,the results are summarized at the end of the paper.
第一章简要回顾了量子信息理论的提出和发展过程,简述了量子纠缠态的提出和定义,并在最后给出了本博士论文的主要研究内容和章节安排。
第二章主要介绍了量子信息的基本理论。首先介绍了EPR佯谬和Bell不等式,几类常见的纠缠态,量子纠缠态的度量,量子不可克隆定理以及几种主要的纠缠操作;然后介绍了几个典型的量子信息处理任务说明量子纠缠作为一个重要的物理资源在量子信息理论中的应用。
第三章主要讨论了利用线性光学元件制备多光子GHZ纠缠态。在这个方案中需要用到简单的线性光学元件,N对两光子极化纠缠态和常规光子探测器。因为实现本方案只需要在探测端口确认是否有光子,而不需要计数光子的数量,所以这就在一定程度上提高了实验上实现的可行性。
第四章主要讨论了量子纠缠态在量子隐形传送方面的应用。两个量子隐形传送方案被提出:第一个方案是利用一个非最大纠缠EPR对作为量子通道来传送N粒子非最大纠缠GHZ态。在这个方案中考虑了量子通道中存在振幅噪音的情况,这个方案可以被推广到传送任意能级N粒子非最大纠缠GHZ态的情况;第二个方案中考虑了利用一维四粒子非最大纠缠Cluster态作为量子通道传送一个任意未知的两比特纠缠态的情况。
第五章主要讨论了量子纠缠态在量子态远程制备中的应用。这一章中,不仅一对一的量子态远程制备的情况被考虑,而且多方联合远程制备量子纠缠态的情况也被考虑。
第六章主要讨论了量子纠缠态在量子秘密共享方面的应用。本章指出,不仅可以用非最大纠缠态作为量子通道实现多方量子秘密共享量子信息,而且利用线性光学的方法也可以实现量子秘密共享量子态。这两种方法的都有各自的优点和缺点。
第七章主要讨论了量子纠缠态在量子安全直接通信方面的应用。本章指出,利用非对称能级的纠缠态作为量子通道可以完美的实现受控量子安全直接通信。这个方案是安全的,高效的,每次信息传送量也大大提高了。而且这个方案可以推广到多方控制情况。
最后给出了全文的总结与展望。
The quantum informatics is an intersection of quantum mechanics and information theory, arisen from 1980s.Over the last two decades,there has been rapid development in both theoretical and experimental studies on quantum information.Quantum entanglement is not only one of the major characteristics that distinguish quantum from classical mechanics, but also an essential ingredient of quantum information theory.As one of the most striking features of quantum formalism,quantum entanglement is used in the field of quantum information as an effective resource.The entanglement has involved many interesting applications without classical counterparts,such as quantum teleportation,quantum dense coding,remote state preparation,quantum secure direct communication,and quantum secret sharing.Therefore,the study of both quantum entanglement and its applications in quantum information theory are necessary and valuable not only to understand well the special properties of the quantum mechanics but also to develop and make use of the new information process methods.Taking the problems stated above into account,theoretical study on preparation of entangled states and their applications in quantum communication are mainly discussed in this dissertation.The thesis has been divided into seven chapters,and our works are included in the chapters from 3 to 7.
In Chapter 1,the background of the study,the proposition and definition of quantum entanglement are introduced,and the major research subjects and the organization of the dissertation are given at the end of this chapter.
In Chapter 2,the basic conception of quantum information is introduced.Firstly,EPR paradox and Bell inequality,and several kinds of entangled states,as well as their properties, are given.Then the measurement of the degree of quantum entanglement,quantum nocloning theorem,and manipulation of quantum entanglement are introduced.At last,several typical quantum information protocols are also introduced in order to demonstrate that quantum entanglement is an important physical resource.
In Chapter 3,the protocol for generating Greenberger-Horne-Zeilinger(GHZ) state of N distant photons with linear optical elements is proposed.The proposed setup consist of simple linear optical elements,N pairs of the two-photon polarization entangled states,and the conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states.This makes the protocol more realizable in experiments.
In chapter 4,the applications of entangled states in quantum teleportation is discussed and two theoretical protocols are developed.In the first protocol,an arbitrary N-qubit GHZ entangled state can be probabilistically teleported from the sender to the receiver via only one non-maximally two qubit entangled state.Without entanglement concentration,using standard Bell-state measurement and classical communication one cannot teleport the state with unit fidelity and unit probability.In the second protocol,an arbitrary and unknown two-qubit entangled state can be probabilistically teleported from the sender to the receiver via a one-dimensional four-particle non-maximally entangled cluster state.By construction, the four-particle state is not reducible to a pair of Bell states.
In chapter 5,the applications of entangled states in remote state preparation is discussed and one theoretical protocol is proposed.In this protocol,one sender and one receiver case, and multiparty remote state preparation(That is two- or multi-party share a quantum state, and they want to remotely prepare it to the receiver) case are considered.
In chapter 6,the applications of entangled states in quantum secret sharing is discussed. A protocol is proposed for multiparty quantum secret sharing via introducing auxiliary particles using a non-maximally entangled two-particle state without a Bell measurement first, and then two optical protocols are proposed for quantum state sharing of superposed coherent states and entangled states,respectively.
In chapter 7,the applications of entangled states in quantum secret direct communication is discussed.A protocol is presented for controlled quantum secure direct communication that uses a 2-dimensional Greenberger-Horne-Zeilinger(GHZ) entangled state and a 3-dimensional Bell-basis state and employs the high-dimensional quantum superdense coding,local collective unitary operations and entanglement swapping.The proposed protocol is secure and of high source capacity.It can effectively protect the communication against a destroying-travelqubit -type attack.With this protocol,the information transmission is greatly increased. This protocol can also be modified,so that it can be used in a multi-party control system.
Finally,the results are summarized at the end of the paper.
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