量子纠缠特性和应用研究
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摘要
20世纪90年代中期Shor量子因子分解算法和Grover量子搜索算法相继被发现,从而使得量子计算与量子信息科学成为研究热点领域。在该领域中,量子纠缠一直扮演着极其重要的角色。事实上,量子纠缠作为量子系统独有的物理特性,不仅能验证量子力学的基本问题,而且是量子计算与量子信息科学中极为重要的资源。因此,研究者从各个方面对量子纠缠进行了研究,例如,量子纠缠的本质、度量、演化和应用,量子纠缠态的分类、制备、传输和存储等。本论文就是围绕着纠缠动力学、纠缠在量子信息处理任务中的应用以及相关实验实现等内容展开研究的,主要目的就是要从理论上进一步理解与利用量子纠缠。本文的主要内容包括:
1.针对具体情形和模型,研究量子纠缠的动力学演化。其一,我们研究了与光腔相作用的原子的纠缠演化,明确给出初态对量子纠缠演化的影响:(1)原子最先制备在GHZ类纯态时,腔中的光子能够在腔内两原子间产生纠缠;(2)原子最先制备在W类纯态时,腔内两原子间的纠缠将会发生突然死亡现象;(3)原子最先制备在混态时,初态中的激发态-基态-基态部分能够在腔内两原子间产生纠缠且缩短零纠缠的时间,而初态中的激发态部分可导致纠缠死亡现象;(4)验证了两个关于Concurrence和负性纠缠的定理。其二,我们采用MABK不等式,考察了三粒子之间的量子非局域性在反铁磁环境下的演化,发现了Bell不等式违背突然不成立的现象和反铁磁环境中的免退相干子空间。其三,研究了在Milburn内在退相干模型中两qutrit系统的纠缠演化,发现纠缠可以通过控制非线性耦合常数来达到最大值。我们上述三个问题的研究结论对延缓、抑制甚至调控环境等引起的量子退相干效应具有重要的意义。
2.研究用纠缠信道完成量子信息处理任务。其一,指出自旋轨道耦合和内在退相干对纠缠传递的影响:发现了一类信道初态,自旋轨道耦合和内在退相干对信道和输出态的纠缠并未产生任何影响,也就是说信道对自旋轨道耦合和内在退相干免疫;而另外一类信道初态,信道和输出态纠缠随自旋轨道耦合和内在退相干的变化而变化。其二,考察了用热纠缠态进行最优的量子密集编码:对两量子比特情形,只有当外加磁场小于自旋耦合系数时热纠缠态才能用来进行密集编码,同时研究了外加磁场和环境温度对密集编码能力的影响并给出了有效的临界编码条件;而对两qutrit系统,它们之间的相互作用系数决定了密集编码的能力且相互作用系数需要大于一定值。我们上述所得结论的意义在于对利用非最大纠缠态进行量子信息处理任务进行了有益的尝试。
3.研究在腔QED中实行两量子比特远程操作的实验方案。我们通过重写恢复算符,得出两量子比特远程操作的方案可以用控制非门和单量子比特门重述,而这些量子门都可以在腔QED中实现,从而论证了在腔QED中实验实现量子远程操作的可行性,并指出了具体的实验步骤。
全文共分四章:第一章对量子纠缠的相关理论进行了简要的介绍;第二章则考虑了环境影响下的纠缠动力学;第三章用纠缠态来完成量子信息处理任务;最后一章给出了在腔QED中实行两量子比特远程操作的实验实现方案。
Because of Shor's factoring algorithm and Grover's searching algorithm in the middle of 1990s,quantum computation and quantum information become one of the important research area.Quantum entanglement is a unique character of quantum system and it can be used not only for testing the basic problem of quantum mechanics but also for acting as an important resource of quantum computation and quantum information.Researchers investigate quantum entanglement carefully,for example,the essential,measurement,evolution and application of entanglement,the classification,preparation,transformation and storage of entanglement.In the thesis,I investigate dynamics of entanglement, application of entanglement in quantum information processing and proposals of realizing quantum information processing in experiment.The aim of the thesis is to understand and discuss entanglement theoretically.The content of the paper is:
1.I study the dynamics of entanglement for different cases.Firstly,I investigate the evolution of entanglement when atoms interact with the cavity and show the effect of initial states on evolution of entanglement.(1)When atoms are initially prepared in GHZ class pure states,photons in the cavity can induce entanglement.(2)When atoms are initially prepared in W class pure states,the phenomenon of entanglement sudden death occurs.(3)When atoms are initially prepared in mixed states,the portion of excited-ground-ground state can induce entanglement and shorten the time of zero entanglement,while the excited state can induce the phenomenon of entanglement sudden death.(4)Furthermore,the model give an example to support two theorems between concurrence and negativity. Secondly,by using of MABK inequality,I investigate the evolution of nonlocality in antiferromagnetic environment.The phenomenon of Bell-nonlocality violation sudden death occurs and the class of decoherence-free states have been found.In the end,I investigate the effect of intrinsic decoherence of Milburn's model on entanglement of two-qutrit states.I could choose the appropriate nonlinear coupling constant to get the maximal entanglement.Study of entanglement dynamics can stave,prevent,or even control the effect of decoherence.
2.I study the application of entangled states in quantum information processing. Firstly,we investigate the Dzyaloshinskill-Moriya anisotropic antisymmetric interaction and intrinsic decoherence on entanglement transfer.For some initial states m|00>+m|11> of the channel,DM interaction and intrinsic decoherence have no effect on the entanglement of the channel and output state.In other words,the channel is immunized from DM interaction and intrinsic decoherence. While for the other initial state 1/2~(1/2)(|01>+|10>) of the channel,DM interaction and intrinsic decoherence have obvious influence on the channel,the entanglement of the output state.Secondly,I study optimal dense coding with thermal entangled states.For two-qubit Heisenberg model,the dense coding capacity is a function of temperature and external magnetic field.Only in the case of external magnetic field being less than the coupling constant,the optimal dense coding can be realized with thermal entangled states.For two-qutrit system,I consider the dense coding capacity taking into account of nonlinear coupling constant and an external magnetic field.I find that the nonlinear coupling constant must be less than 0 for dense coding.I try to implement quantum information processing by using non-maximally entangled states.
3.I show the proposal for remote implementation of partially unknown quantum operations of two qubits in cavity QED.By constructing the recovery operations of the protocol of remote implementation of partially unknown quantum operation of two qubits[An Min Wang:Phys.Rev.A 74(2006) 032317] with two-qubit Cnot gate and single qubit logic gates,all the quantum gates can be realized in cavity QED.Based on these,I present a scheme to implement remeote implementation of partially unknown quantum operations of two qubits in cavity QED.
The thesis consists of four parts.In chapter 1,I introduce the relative theory of entanglement in quantum computation and quantum information.In chapter 2,the dynamics of entanglement in environment is investigated.In chapter 3,I investigate the application of entanglement in quantum information processing. In the last chapter,the scheme for remote implementation of partially unknown quantum operation of two qubits in cavity QED is shown.
1.针对具体情形和模型,研究量子纠缠的动力学演化。其一,我们研究了与光腔相作用的原子的纠缠演化,明确给出初态对量子纠缠演化的影响:(1)原子最先制备在GHZ类纯态时,腔中的光子能够在腔内两原子间产生纠缠;(2)原子最先制备在W类纯态时,腔内两原子间的纠缠将会发生突然死亡现象;(3)原子最先制备在混态时,初态中的激发态-基态-基态部分能够在腔内两原子间产生纠缠且缩短零纠缠的时间,而初态中的激发态部分可导致纠缠死亡现象;(4)验证了两个关于Concurrence和负性纠缠的定理。其二,我们采用MABK不等式,考察了三粒子之间的量子非局域性在反铁磁环境下的演化,发现了Bell不等式违背突然不成立的现象和反铁磁环境中的免退相干子空间。其三,研究了在Milburn内在退相干模型中两qutrit系统的纠缠演化,发现纠缠可以通过控制非线性耦合常数来达到最大值。我们上述三个问题的研究结论对延缓、抑制甚至调控环境等引起的量子退相干效应具有重要的意义。
2.研究用纠缠信道完成量子信息处理任务。其一,指出自旋轨道耦合和内在退相干对纠缠传递的影响:发现了一类信道初态,自旋轨道耦合和内在退相干对信道和输出态的纠缠并未产生任何影响,也就是说信道对自旋轨道耦合和内在退相干免疫;而另外一类信道初态,信道和输出态纠缠随自旋轨道耦合和内在退相干的变化而变化。其二,考察了用热纠缠态进行最优的量子密集编码:对两量子比特情形,只有当外加磁场小于自旋耦合系数时热纠缠态才能用来进行密集编码,同时研究了外加磁场和环境温度对密集编码能力的影响并给出了有效的临界编码条件;而对两qutrit系统,它们之间的相互作用系数决定了密集编码的能力且相互作用系数需要大于一定值。我们上述所得结论的意义在于对利用非最大纠缠态进行量子信息处理任务进行了有益的尝试。
3.研究在腔QED中实行两量子比特远程操作的实验方案。我们通过重写恢复算符,得出两量子比特远程操作的方案可以用控制非门和单量子比特门重述,而这些量子门都可以在腔QED中实现,从而论证了在腔QED中实验实现量子远程操作的可行性,并指出了具体的实验步骤。
全文共分四章:第一章对量子纠缠的相关理论进行了简要的介绍;第二章则考虑了环境影响下的纠缠动力学;第三章用纠缠态来完成量子信息处理任务;最后一章给出了在腔QED中实行两量子比特远程操作的实验实现方案。
Because of Shor's factoring algorithm and Grover's searching algorithm in the middle of 1990s,quantum computation and quantum information become one of the important research area.Quantum entanglement is a unique character of quantum system and it can be used not only for testing the basic problem of quantum mechanics but also for acting as an important resource of quantum computation and quantum information.Researchers investigate quantum entanglement carefully,for example,the essential,measurement,evolution and application of entanglement,the classification,preparation,transformation and storage of entanglement.In the thesis,I investigate dynamics of entanglement, application of entanglement in quantum information processing and proposals of realizing quantum information processing in experiment.The aim of the thesis is to understand and discuss entanglement theoretically.The content of the paper is:
1.I study the dynamics of entanglement for different cases.Firstly,I investigate the evolution of entanglement when atoms interact with the cavity and show the effect of initial states on evolution of entanglement.(1)When atoms are initially prepared in GHZ class pure states,photons in the cavity can induce entanglement.(2)When atoms are initially prepared in W class pure states,the phenomenon of entanglement sudden death occurs.(3)When atoms are initially prepared in mixed states,the portion of excited-ground-ground state can induce entanglement and shorten the time of zero entanglement,while the excited state can induce the phenomenon of entanglement sudden death.(4)Furthermore,the model give an example to support two theorems between concurrence and negativity. Secondly,by using of MABK inequality,I investigate the evolution of nonlocality in antiferromagnetic environment.The phenomenon of Bell-nonlocality violation sudden death occurs and the class of decoherence-free states have been found.In the end,I investigate the effect of intrinsic decoherence of Milburn's model on entanglement of two-qutrit states.I could choose the appropriate nonlinear coupling constant to get the maximal entanglement.Study of entanglement dynamics can stave,prevent,or even control the effect of decoherence.
2.I study the application of entangled states in quantum information processing. Firstly,we investigate the Dzyaloshinskill-Moriya anisotropic antisymmetric interaction and intrinsic decoherence on entanglement transfer.For some initial states m|00>+m|11> of the channel,DM interaction and intrinsic decoherence have no effect on the entanglement of the channel and output state.In other words,the channel is immunized from DM interaction and intrinsic decoherence. While for the other initial state 1/2~(1/2)(|01>+|10>) of the channel,DM interaction and intrinsic decoherence have obvious influence on the channel,the entanglement of the output state.Secondly,I study optimal dense coding with thermal entangled states.For two-qubit Heisenberg model,the dense coding capacity is a function of temperature and external magnetic field.Only in the case of external magnetic field being less than the coupling constant,the optimal dense coding can be realized with thermal entangled states.For two-qutrit system,I consider the dense coding capacity taking into account of nonlinear coupling constant and an external magnetic field.I find that the nonlinear coupling constant must be less than 0 for dense coding.I try to implement quantum information processing by using non-maximally entangled states.
3.I show the proposal for remote implementation of partially unknown quantum operations of two qubits in cavity QED.By constructing the recovery operations of the protocol of remote implementation of partially unknown quantum operation of two qubits[An Min Wang:Phys.Rev.A 74(2006) 032317] with two-qubit Cnot gate and single qubit logic gates,all the quantum gates can be realized in cavity QED.Based on these,I present a scheme to implement remeote implementation of partially unknown quantum operations of two qubits in cavity QED.
The thesis consists of four parts.In chapter 1,I introduce the relative theory of entanglement in quantum computation and quantum information.In chapter 2,the dynamics of entanglement in environment is investigated.In chapter 3,I investigate the application of entanglement in quantum information processing. In the last chapter,the scheme for remote implementation of partially unknown quantum operation of two qubits in cavity QED is shown.
引文
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