量子关联的动力学研究
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摘要
在最近的十年来,量子信息处理把量子力学原理与信息科学相结合已经在诸多领域有所发展.这既给量子物理,同时也给计算机科学发展带来了新的视角和动力.在我的博士论文中,主要关注在不同的退相干模型下的量子关联的动力学演化.纠缠作为量子信息处理所需的重要资源,对其的研究已经持续了很多年.最近,人们对于量子关联的研究兴趣渐起,其中最为关注的是利用QuantumDiscord来度量量子关联.对于这个领域,我们的工作如下:
(1).研究了一个任意的,具有相同纠缠度的两体纠缠初始纯态,分别在退相位通道和振幅衰减通道(Amplitude damping channel)下,态的纠缠动力学演化过程.通过解析计算和分析,得到了纠缠衰减过程的解析表达式.同时,我们还给出了对于任意纯态经历通道后,其解纠缠的一个下却界.
(2).针对目前研究最多的Quantum Discord度量,我们利用一种几何描述的方式,形象的刻画了对于一个两体X-type的量子态,其最优的测量方式在布洛赫球(Bloch Sphere)上的分解形式,利用这个分解方式,为我们计算QuantumDiscord带来了一定的简化.同时,利用这个几何描述,研究了上述态通过量子噪声通道时,解释了量子关联与经典关联在通道演化过程中突变的原因.同时,根据Koashi-Winter关系,利用纯化方式,我们分析了任意的秩(Rank)为2的两体态的Discord,并且给出了解析表达公式,这是第一次给出了这类态的Discord的解析式.最后,我们又具体的针对一个任意2×2纯态,研究其经历单侧通道的动力学演化.
(3).在我们的工作中,研究了一个基于固态自旋-微腔耦合体系的模型,在这个模型当中,系统同时与周围的核自旋热库和腔内的单模腔场有相互作用.在这个理想模型中我们假设整个体系处在强磁场下,因此固态自旋与核自旋热库认为是伊辛模型(Ising Model)相互作用;同时,核自旋热库与腔场的相互作用可以忽略.我们还利用量子马尔可夫主方程,来研究共同热库下的初始为两体直积态的量子关联与量子纠缠的动力学演化.我们注意到,在这样的一个共同热库作用下,初始的Quantum Discord从零开始增加,而纠缠始终为零.
Quantum information processing, which is combined the quantum mechanics andthe information science, have developed fast over the past decades. These bring newviewpointstobothPhysicsandComputing. Inthisdissertation, wefocusonthedynam-ics evolution of quantum correlation in different decoherence models. We have knownthat the entanglement is important for quantum information processing. Recently, theresearch of quantum correlation, often measured by quantum discord, attract numerousattentions. Our works on this field are as follows:
(1). We presented an analytic result for the entanglement evolution for arbitrarytwo-qubit pure state under amplitude damping and particularly phase damping channel.The disentanglement time and the relationship between it and the form of initial stateare given explicitly. The lower bounds of disentanglement time are obtained and shownto be the monotone functions of initial concurrence.
(2). We reveal a relationship between the original definition of discord base on themeasurementsandthegeometricviewpointwithnoneedformeasurements,fromwhichtwo-qubit quantum discord can be described clearly. The known results about X statediscord are restated in the directly perceivable geometric language. As a consequence,thedynamicsofclassicalcorrelationsandquantumdiscordforanXstateinthepresenceofdecoherenceisendowedwithgeometricinterpretation. Wealsodiscussedthoroughlythecaseoftwo-qubitrank-twostates. Ananalyticalexpressionforthequantumdiscordis obtained by means of Koashi-Winter relation. At last, we discuss the dynamicalevolution of arbitrary 2-qubit pure states through a one-sided channel.
(3). We study dynamical evolution of a solid-spin state surrounded by a nuclearspin-bathinamicro-cavity. Inthesimplifiedmodel,weassumetheinteractionsbetweenthe system spin and the bath are Ising coupling, and there is no interaction between thespin-bath and the optical field in the cavity. We also investigate quantum correlationdynamical evolutions of a two-qubit state immersed a common bath by using a Marko-vian quantum master equation, and we find the quantum discord still exist even thoughthe entanglement is absent thoroughly in the evolution.
(1).研究了一个任意的,具有相同纠缠度的两体纠缠初始纯态,分别在退相位通道和振幅衰减通道(Amplitude damping channel)下,态的纠缠动力学演化过程.通过解析计算和分析,得到了纠缠衰减过程的解析表达式.同时,我们还给出了对于任意纯态经历通道后,其解纠缠的一个下却界.
(2).针对目前研究最多的Quantum Discord度量,我们利用一种几何描述的方式,形象的刻画了对于一个两体X-type的量子态,其最优的测量方式在布洛赫球(Bloch Sphere)上的分解形式,利用这个分解方式,为我们计算QuantumDiscord带来了一定的简化.同时,利用这个几何描述,研究了上述态通过量子噪声通道时,解释了量子关联与经典关联在通道演化过程中突变的原因.同时,根据Koashi-Winter关系,利用纯化方式,我们分析了任意的秩(Rank)为2的两体态的Discord,并且给出了解析表达公式,这是第一次给出了这类态的Discord的解析式.最后,我们又具体的针对一个任意2×2纯态,研究其经历单侧通道的动力学演化.
(3).在我们的工作中,研究了一个基于固态自旋-微腔耦合体系的模型,在这个模型当中,系统同时与周围的核自旋热库和腔内的单模腔场有相互作用.在这个理想模型中我们假设整个体系处在强磁场下,因此固态自旋与核自旋热库认为是伊辛模型(Ising Model)相互作用;同时,核自旋热库与腔场的相互作用可以忽略.我们还利用量子马尔可夫主方程,来研究共同热库下的初始为两体直积态的量子关联与量子纠缠的动力学演化.我们注意到,在这样的一个共同热库作用下,初始的Quantum Discord从零开始增加,而纠缠始终为零.
Quantum information processing, which is combined the quantum mechanics andthe information science, have developed fast over the past decades. These bring newviewpointstobothPhysicsandComputing. Inthisdissertation, wefocusonthedynam-ics evolution of quantum correlation in different decoherence models. We have knownthat the entanglement is important for quantum information processing. Recently, theresearch of quantum correlation, often measured by quantum discord, attract numerousattentions. Our works on this field are as follows:
(1). We presented an analytic result for the entanglement evolution for arbitrarytwo-qubit pure state under amplitude damping and particularly phase damping channel.The disentanglement time and the relationship between it and the form of initial stateare given explicitly. The lower bounds of disentanglement time are obtained and shownto be the monotone functions of initial concurrence.
(2). We reveal a relationship between the original definition of discord base on themeasurementsandthegeometricviewpointwithnoneedformeasurements,fromwhichtwo-qubit quantum discord can be described clearly. The known results about X statediscord are restated in the directly perceivable geometric language. As a consequence,thedynamicsofclassicalcorrelationsandquantumdiscordforanXstateinthepresenceofdecoherenceisendowedwithgeometricinterpretation. Wealsodiscussedthoroughlythecaseoftwo-qubitrank-twostates. Ananalyticalexpressionforthequantumdiscordis obtained by means of Koashi-Winter relation. At last, we discuss the dynamicalevolution of arbitrary 2-qubit pure states through a one-sided channel.
(3). We study dynamical evolution of a solid-spin state surrounded by a nuclearspin-bathinamicro-cavity. Inthesimplifiedmodel,weassumetheinteractionsbetweenthe system spin and the bath are Ising coupling, and there is no interaction between thespin-bath and the optical field in the cavity. We also investigate quantum correlationdynamical evolutions of a two-qubit state immersed a common bath by using a Marko-vian quantum master equation, and we find the quantum discord still exist even thoughthe entanglement is absent thoroughly in the evolution.
引文
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[47] Ficek Z and Tanas R Phys. Rev. A 74 024304, 2006
[48] Li Zeng-Zhao, Liang Xian-Ting and Pan Xiao-Yin Phys. Lett. A 373, 2009 4028
[49] Rau A R P, Ali M and Alber G Europhys. Lett. 82 40002, 2008
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[55] C E Lopez, G Romero, F Lastra,2 E Solano and J C Retamal, Phys. Rev. Lett. 101 080503, 2008.
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