量子光学系统的纠缠及其应用
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摘要
作为量子通信不可替代的资源，纠缠系统在量子信息处理中发挥着重要的作用。纠缠光子系统和纠缠相干态是两种可实现量子比特，可进行量子通信的重要载体。相对其他实现量子信息处理的载体，它们易于制备，并可在自由空间传播的特点，使得它们在量子信息处理中受到极大的关注。
纠缠的产生与测量是量子信息处理的基础，是实现量子密钥分配、量子隐形传态、量子机密共享的关键。利用克尔介质产生纠缠相干态是实现纠缠的重要方式。耗散及退相干会影响产生的纠缠态的保真度，降低产生效率和成功率。利用线性光学无法进行完全光子纠缠态分析，但利用超纠缠态可以解决这个难题。本博士论文主要研究纠缠相干态的产生和光子纠缠态分析，研究结果如下：
第一，本文提出了利用单光子或纠缠光子辅助多模相干态通过非线性克尔介质、分束器和偏振分束器等光学器件产生多模纠缠相干态的方案。利用这一模型分别产生了贝尔型纠缠相干态、GHZ型纠缠相干态和W型纠缠相干态，并考虑存在光子耗散、探测器效率低下和相干态能量损失情况时，它们带来的退相干效应对三种纠缠相干态产生的影响。系统地计算和讨论了贝尔纠缠态的保真度、振幅等随退相干效应和输入态振幅的变化关系，并利用Concurrence和Negativity对产生的贝尔纠缠相干态进行纠缠度量，给出了纠缠度随输入态振幅的变化关系。
第二，本文提出了一类新的多模纠缠相干态，即：χ型纠缠相干态，并给出了产生方案。另外讨论了这类态的Bell型不等式的违背情况，给出了最大违背随纠缠相干态振幅的关系曲线图。χ型纠缠相干态在小振幅区域出现很好的违背，显示出极强的纠缠特性。
第三，本文利用超纠缠对光子GHZ态进行了纠缠态分析。首先利用光子动量自由度辅助实现三光子偏振GHZ态分析。偏振-动量超纠缠光子依次经过偏振分束器的CNOT操作、半波片的Hadamard操作和偏振态分析器，根据探测器的响应情况可以100%地区分所有的多光子GHZ偏振纠缠态。另外利用偏振自由度实现了三光子动量自由度GHZ纠缠态分析。最后给出了分析方案的多光子推广。
As an irreplaceable source for quantum communication, entangled system play ansignificant role in quantum information processing. Entangled photons and entangledcoherentstates(ECS)aretwocrucialwaysinrealizationofquantumqubitsandimportantinformation carriers. In contrast to other systems of quantum information processing,they are easy to be prepared, and can travel in free space as flying qubits, which makesthem prominent in quantum information processing.
Generation and measurement of entanglement are the bases of quantum informa-tion processing and the key points of quantum key distribution, quantum teleportation,quantum secret sharing, etc. Generation of ECSs by using Kerr nonlinearity is a crucialway in entanglement generation. Dissipation and decoherence will decrease the fideli-ty of entanglement, affect the production efficiency and the success probability. Usinglinear optical elements is unable to completely analyze photonic entanglement, but thisproblem can be solved through hyper-entanglement. The main point of this article ishow to generate ECSs and analyze photon entangled states, the results are as follows:
First, this paper propose a protocol of generating multi-mode ECSs by nonlinearKerr medium, beam splitter and polarizing beam splitter assisted by single photon orentangled photons. And Bell-type, GHZ-type and W-type ECSs are generated. The pro-tocols are investigated with considering the decoherence caused by the dissipation ofphotons, low efficiency of detector and energy loss of coherent state. The entanglementfidelity, amplitude and others with the decoherence and the amplitude of input state aresystematically calculated and discussed. The entanglement of generated ECS are quan-tified through Concurrence and Negativity, and the results are plotted with the amplitudeof input state.
Second, this paper presents a new type of multi-mode ECS, namely, χ-type ECS,and propose a protocol of generation with Kerr nonlinearity. And Bell-type inequalitywith respect to χ-type ECS is investigated, the optimal violation against with the am-plitude of χ-type ECS is calculated. The results show strong violation occurs in smallamplitude region.
Third, multi-photon GHZ state analysis using hyperentangled states is proposed.Firstly the polarization three-photon GHZ states are analyzed assisted by the degree of freedom of momentum. The photons are transformed by polarization beam splitters andhalf-wave plates which make CNOT and Hadamard operations, then go to the polariza-tion analyzers. According to the response of the detector, the polarization GHZ statescanbe100%distinguished. Theschemeisimplementableusingpresent-daytechnology.Further analysis of three-photon GHZ states in degree of freedom of momentum is in-vestigated, which results the states can be distinguished clearly with ancillary degree offreedomofpolarization. Finally, theprotocolisprovedtobegeneralizedtomulti-photonsituation.
纠缠的产生与测量是量子信息处理的基础，是实现量子密钥分配、量子隐形传态、量子机密共享的关键。利用克尔介质产生纠缠相干态是实现纠缠的重要方式。耗散及退相干会影响产生的纠缠态的保真度，降低产生效率和成功率。利用线性光学无法进行完全光子纠缠态分析，但利用超纠缠态可以解决这个难题。本博士论文主要研究纠缠相干态的产生和光子纠缠态分析，研究结果如下：
第一，本文提出了利用单光子或纠缠光子辅助多模相干态通过非线性克尔介质、分束器和偏振分束器等光学器件产生多模纠缠相干态的方案。利用这一模型分别产生了贝尔型纠缠相干态、GHZ型纠缠相干态和W型纠缠相干态，并考虑存在光子耗散、探测器效率低下和相干态能量损失情况时，它们带来的退相干效应对三种纠缠相干态产生的影响。系统地计算和讨论了贝尔纠缠态的保真度、振幅等随退相干效应和输入态振幅的变化关系，并利用Concurrence和Negativity对产生的贝尔纠缠相干态进行纠缠度量，给出了纠缠度随输入态振幅的变化关系。
第二，本文提出了一类新的多模纠缠相干态，即：χ型纠缠相干态，并给出了产生方案。另外讨论了这类态的Bell型不等式的违背情况，给出了最大违背随纠缠相干态振幅的关系曲线图。χ型纠缠相干态在小振幅区域出现很好的违背，显示出极强的纠缠特性。
第三，本文利用超纠缠对光子GHZ态进行了纠缠态分析。首先利用光子动量自由度辅助实现三光子偏振GHZ态分析。偏振-动量超纠缠光子依次经过偏振分束器的CNOT操作、半波片的Hadamard操作和偏振态分析器，根据探测器的响应情况可以100%地区分所有的多光子GHZ偏振纠缠态。另外利用偏振自由度实现了三光子动量自由度GHZ纠缠态分析。最后给出了分析方案的多光子推广。
As an irreplaceable source for quantum communication, entangled system play ansignificant role in quantum information processing. Entangled photons and entangledcoherentstates(ECS)aretwocrucialwaysinrealizationofquantumqubitsandimportantinformation carriers. In contrast to other systems of quantum information processing,they are easy to be prepared, and can travel in free space as flying qubits, which makesthem prominent in quantum information processing.
Generation and measurement of entanglement are the bases of quantum informa-tion processing and the key points of quantum key distribution, quantum teleportation,quantum secret sharing, etc. Generation of ECSs by using Kerr nonlinearity is a crucialway in entanglement generation. Dissipation and decoherence will decrease the fideli-ty of entanglement, affect the production efficiency and the success probability. Usinglinear optical elements is unable to completely analyze photonic entanglement, but thisproblem can be solved through hyper-entanglement. The main point of this article ishow to generate ECSs and analyze photon entangled states, the results are as follows:
First, this paper propose a protocol of generating multi-mode ECSs by nonlinearKerr medium, beam splitter and polarizing beam splitter assisted by single photon orentangled photons. And Bell-type, GHZ-type and W-type ECSs are generated. The pro-tocols are investigated with considering the decoherence caused by the dissipation ofphotons, low efficiency of detector and energy loss of coherent state. The entanglementfidelity, amplitude and others with the decoherence and the amplitude of input state aresystematically calculated and discussed. The entanglement of generated ECS are quan-tified through Concurrence and Negativity, and the results are plotted with the amplitudeof input state.
Second, this paper presents a new type of multi-mode ECS, namely, χ-type ECS,and propose a protocol of generation with Kerr nonlinearity. And Bell-type inequalitywith respect to χ-type ECS is investigated, the optimal violation against with the am-plitude of χ-type ECS is calculated. The results show strong violation occurs in smallamplitude region.
Third, multi-photon GHZ state analysis using hyperentangled states is proposed.Firstly the polarization three-photon GHZ states are analyzed assisted by the degree of freedom of momentum. The photons are transformed by polarization beam splitters andhalf-wave plates which make CNOT and Hadamard operations, then go to the polariza-tion analyzers. According to the response of the detector, the polarization GHZ statescanbe100%distinguished. Theschemeisimplementableusingpresent-daytechnology.Further analysis of three-photon GHZ states in degree of freedom of momentum is in-vestigated, which results the states can be distinguished clearly with ancillary degree offreedomofpolarization. Finally, theprotocolisprovedtobegeneralizedtomulti-photonsituation.
引文
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