量子纠缠态的制备、应用及非局域性
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摘要
量子信息学已经成为过去二十年来兴起的最激动人心的科学进展之一。由量子信息学而新兴的技术发展,诸如量子密码、量子通信和量子计算等引起了物理学家、数学家、计算机专家、电子工程师等众多领域的专家的广泛关注。量子纠缠现象是量子力学独特的资源,是量子隐形传态、快速量子算法和量子纠错等效应中的关键因素,在量子计算与量子信息的应用中起着关键作用,因此驾驭它的规律用途,寻求对它定性和定量的描述正成为一个新兴的研究方向。本文正是致力于量子纠缠的制备、应用及非局域性的分析和研究。
本文结构安排如下:
第一章为绪论,简要介绍量子信息学的基础知识和一些基于量子纠缠的重要应用。
第二章简单回顾关于量子纠缠的基本概念,包括量子纠缠的数学描述、两体纠缠判据和量子纠缠度。
第三章简要介绍几类常见的量子纠缠态及它们的性质和应用。
第四章,利用电荷奇偶性测量提出了在自由电子体系中实现量子隐形传态和基于纠缠交换的纠缠浓缩的线性光学方案。另外,利用费米子极化分束器、费米子单比特旋转和电荷奇偶性测量相结合的办法,可以确定性地产生一些典型的纠缠态,如GHZ态、W态、团簇态等。此方案是确定性的,成功概率为100%,无需以前线性光学方案中所需的联合Bell基测量。
第五章,基于电子和单模腔的相互作用,展示了如何制备团簇型纠缠相干态和N电子的W态。在该方案中,还进一步研究了团簇型纠缠相干态的非局域性质和腔一电子系统在含腔损耗下的时间演化特性。
第六章,详细阐述了GHZ实验最基本的内涵:一组非局域可观测量有一个公共本征态使得它们在这个态上的取值与用EPR的局域实在性给出的结论是矛盾的。众所周知,原始的GHZ-Mermin型的证明在局域酉等价下只有一种形式。研究表明,将若干个量子位视为整体并且构造新的类Pauli算符,得到一维晶格体系中四体团簇态和五体团簇态的GHZ实验分别存在8种和48种不同的形式.这种方法很容易推广到N体体系,我们继而研究与之对应的Bell算符,使得它只在N体团簇态上达到最大违背。因此,我们完整地构造一维晶格体系中N体团簇态的GHZ定理。
第七章给出结论和一些尚待解决的问题。
Quantum information science has emerged as one of the most exciting scientific developments of the past twenty years.The new technological prospects of quantum information in quantum cryptograph,quantum communication and quantum computation attract not only physicists but also researchers from other scientific communities, mainly mathematicians,computer scientists and electrical engineers.Quantum entanglement is a special quantum mechanical resource that plays a key role in many applications of quantum computation and quantum information,it is a key element in effects such as quantum teleportation,fast quantum algorithms,and quantum error-correction. As a result,there is a thriving research community in finding principles which govern its manipulation,utilization and its quantitative and qualitative description,This thesis is a contribution to the analysis on the preparation,application and nonlocality of the entangled states.
The structure of this thesis is as follows:
Chapter 1 is the exordium.I simply introduce the general knowledge about quantum information and some important applications based on quantum entanglement.
In Chapter 2 I review basic aspects of entanglement including its mathematical description,inseparable criterion and entanglement measure.
In Chapter 3 I briefly introduce several common quantum entangled states and study their properties and applications.
In Chapter 4 an attempt is made to propose a electronic linear optical scheme for the teleportation and entanglement concentration via entanglement swapping based on charge detection.I also prove that this method is useful in generating entangled states such as GHZ states,W states,and cluster states using fermionic polarizing beam splitters and single spin rotations assisted by parity check on the fermionic qubits.Our scheme is nearly deterministic(i.e.,with 100%success probability) and does not need the joint Bell state measurement required in the previous schemes.
In Chapter 5 I propose a method of generating the cluster-type entangled coherent states(CTECS) and the W state through the cavity-electron interaction.Furthermore, I investigate the nonlocal properties of the generated CTECS and the time evolution of the electron-cavity system involving cavity decay.
In Chapter 6,Greenberger-Horne-Zeilinger(GHZ) theorem constitutes that there is a set of mutually commuting nonlocal observables with a common eigenstate on which those observables assume values that refute the attempt to assign values only required to have them by the local realism of Einstein,Podolsky,and Rosen(EPR).It is known that there is only one form of the GHZ-Mermin-like argument with equivalence up to a local unitary transformation.However,we show that there are eight distinct forms of the Greenberger-Horne-Zeilinger(GHZ) argument for the four-qubit cluster state and forty eight distinct forms for the five-qubit cluster state in the case of the onedimensional lattice.The proof is obtained by regarding the pair qubits as a single object and constructing the new Pauli-like operators.The method can be easily extended to the case of the N-qubit system and the associated Bell operator are also discussed, on which only cluster states assume its maximum value.Consequently,we present a complete construction of the GHZ theorem for the cluster states of N-qubit in the case of the one-dimensional lattice.
Summary and some open problems are given in Chapter 7.
本文结构安排如下:
第一章为绪论,简要介绍量子信息学的基础知识和一些基于量子纠缠的重要应用。
第二章简单回顾关于量子纠缠的基本概念,包括量子纠缠的数学描述、两体纠缠判据和量子纠缠度。
第三章简要介绍几类常见的量子纠缠态及它们的性质和应用。
第四章,利用电荷奇偶性测量提出了在自由电子体系中实现量子隐形传态和基于纠缠交换的纠缠浓缩的线性光学方案。另外,利用费米子极化分束器、费米子单比特旋转和电荷奇偶性测量相结合的办法,可以确定性地产生一些典型的纠缠态,如GHZ态、W态、团簇态等。此方案是确定性的,成功概率为100%,无需以前线性光学方案中所需的联合Bell基测量。
第五章,基于电子和单模腔的相互作用,展示了如何制备团簇型纠缠相干态和N电子的W态。在该方案中,还进一步研究了团簇型纠缠相干态的非局域性质和腔一电子系统在含腔损耗下的时间演化特性。
第六章,详细阐述了GHZ实验最基本的内涵:一组非局域可观测量有一个公共本征态使得它们在这个态上的取值与用EPR的局域实在性给出的结论是矛盾的。众所周知,原始的GHZ-Mermin型的证明在局域酉等价下只有一种形式。研究表明,将若干个量子位视为整体并且构造新的类Pauli算符,得到一维晶格体系中四体团簇态和五体团簇态的GHZ实验分别存在8种和48种不同的形式.这种方法很容易推广到N体体系,我们继而研究与之对应的Bell算符,使得它只在N体团簇态上达到最大违背。因此,我们完整地构造一维晶格体系中N体团簇态的GHZ定理。
第七章给出结论和一些尚待解决的问题。
Quantum information science has emerged as one of the most exciting scientific developments of the past twenty years.The new technological prospects of quantum information in quantum cryptograph,quantum communication and quantum computation attract not only physicists but also researchers from other scientific communities, mainly mathematicians,computer scientists and electrical engineers.Quantum entanglement is a special quantum mechanical resource that plays a key role in many applications of quantum computation and quantum information,it is a key element in effects such as quantum teleportation,fast quantum algorithms,and quantum error-correction. As a result,there is a thriving research community in finding principles which govern its manipulation,utilization and its quantitative and qualitative description,This thesis is a contribution to the analysis on the preparation,application and nonlocality of the entangled states.
The structure of this thesis is as follows:
Chapter 1 is the exordium.I simply introduce the general knowledge about quantum information and some important applications based on quantum entanglement.
In Chapter 2 I review basic aspects of entanglement including its mathematical description,inseparable criterion and entanglement measure.
In Chapter 3 I briefly introduce several common quantum entangled states and study their properties and applications.
In Chapter 4 an attempt is made to propose a electronic linear optical scheme for the teleportation and entanglement concentration via entanglement swapping based on charge detection.I also prove that this method is useful in generating entangled states such as GHZ states,W states,and cluster states using fermionic polarizing beam splitters and single spin rotations assisted by parity check on the fermionic qubits.Our scheme is nearly deterministic(i.e.,with 100%success probability) and does not need the joint Bell state measurement required in the previous schemes.
In Chapter 5 I propose a method of generating the cluster-type entangled coherent states(CTECS) and the W state through the cavity-electron interaction.Furthermore, I investigate the nonlocal properties of the generated CTECS and the time evolution of the electron-cavity system involving cavity decay.
In Chapter 6,Greenberger-Horne-Zeilinger(GHZ) theorem constitutes that there is a set of mutually commuting nonlocal observables with a common eigenstate on which those observables assume values that refute the attempt to assign values only required to have them by the local realism of Einstein,Podolsky,and Rosen(EPR).It is known that there is only one form of the GHZ-Mermin-like argument with equivalence up to a local unitary transformation.However,we show that there are eight distinct forms of the Greenberger-Horne-Zeilinger(GHZ) argument for the four-qubit cluster state and forty eight distinct forms for the five-qubit cluster state in the case of the onedimensional lattice.The proof is obtained by regarding the pair qubits as a single object and constructing the new Pauli-like operators.The method can be easily extended to the case of the N-qubit system and the associated Bell operator are also discussed, on which only cluster states assume its maximum value.Consequently,we present a complete construction of the GHZ theorem for the cluster states of N-qubit in the case of the one-dimensional lattice.
Summary and some open problems are given in Chapter 7.
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