开放量子系统的量子失协冻结研究
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摘要
探索退相干效应对相关单量子态调控方案实现的破坏作用及其有效的抑制策略是近年来量子调控研究的核心问题,实验技术的不断提高也迫切要求发展微观系统退相干超越传统Born-Markovian近似的描述方案并发掘non-Markovian效应所诱导的新物理。另一方面,随着量子信息科学研究的不断深入,人们发现量子纠缠并不能穷尽量子关联,.量子关联被一种称作量子失协的量所更普遍的刻画；探索量子失协在具体量子信息处理协议中与量子纠缠定量甚至是定性的不同是近年来量子信息研究的热点问题之一。受这两方面研究的启发,我们在本文中研究了如下几类系统在不同退相干模型中的non-Markovian动力学问题：
首先,我们研究了两个初始具有量子关联的分立变量系统在两个独立退相位噪声中的non-Markovian关联动力学。我们发现不同于量子纠缠渐进单调地趋于零的行为,系统的量子失协和经典关联在演化过程中存在一个从经典退相干到量子退相干的转变时刻,在该时刻之前,系统处在经典退相干区,此时退相位将使得量子失协在有限的时间内冻结在其初始值上,而经典关联发生衰减；在该时刻之后,系统处在量子退相干区,此时退相位将使得经典关联保持不变,而量子失协开始衰减并最终趋于零。在这个模型中,non-Markovian效应并没有对该量子关联演化行为带来定性的影响。
其次,我们研究了两个初始具有量子关联的连续变量系统在两个独立的耗散噪声中的non-Markovian关联动力学。我们发现：non-Markovian效应将使得初态中的量子失协部分地永久冻结在其长时稳态上,该结果与基于Born-Markovian近似下量子失协渐进地趋于零的结果具有定性的不同,说明此时Born-Markovian近似已不能描述系统的退相干行为；进一步的分析表明,量子失协的该持久冻结机制来源于各子系统与其环境形成一个耦合的局域化模式,根据此机制,我们给出了量子失协永久冻结的定量判据,该判据揭示出我们可以通过调控系统与环境的耦合以及环境的谱密度来对退相干进行抑制,为从实验上实现退相干的抑制提供了新的方法。
最后,我们研究了两个初始没有量子关联的分立变量系统,其中之一受到局域耗散噪声环境影响的关联动力学。我们发现：在non-Markovian动力学下,该耗散噪声不仅能够瞬时地诱导出量子系统之间的量子失协,而且能够使得该量子失协免受进一步的退相干影响以保持到其长时稳态,该结果与以前文献中基于Born-Markovian近似的该瞬时诱导出的量子失协渐进地趋于零的结果具有定性的不同；揭示了不诉诸于直接或间接相互作用,通过单个局域的耗散噪声来制备量子系统之间稳定量子失协的物理策略。分析表明：该稳定的量子失协制备同样决定于系统与其耦合环境束缚态形成的物理判据,我们所得到的解析判据为从实验上制备各子系统之间稳定的量子失协提供了理论依据。
我们的结果系统地展示了non-Markovian效应在具体量子信息处理中的显著作用,也反映了量子失协与量子纠缠在刻画量子关联中定性的不同；我们所发现的系统与环境束缚态／耦合局域模式的形成所导致的退相干抑制为实验上探索退相干控制方案提供了新的策略。
It is one of the crucial issues in quantum engineering field to evaluate the detrimental impacts of decoherence on the schemes of the single-quantum-state control and exploring its efficient suppression strategy. The rapid development of the experimental technique in this field also asks for the establishment of the general description to the decoherence going beyond the widely-used Born-Markovian approximation and the pursuit of the new physics induced by the non-Markovian effect in explicit physical systems. On the other hand, it is found that quantum entanglement cannot exhaust all the characters of quantum correlation, and quantum correlation can be characterized by the so-called quantum discord in a more general way than the quantum entanglement. Therefore, the study on exploring the quantitative or even qualitative difference between quantum discord and quantum entanglement in the protocols of quantum information processing is a hot topics in quantum information science recently. Motivated by these two aspects, we study in this thesis the non-Markovian correlation dynamics of the following several systems influenced by different type of decoherence channels:
Firstly, we study the non-Markovian correlation dynamics of two initially quantum corre-lated discrete-variable systems immersed in two independent dephasing noises. It is found that much different from the behavior of the monotonic decay to zero of quantum entanglement, the behavior of quantum discord and classical correlation shows a transition behavior at certain time from classical decoherence to quantum decoherence. Before this time, the system is in classical decoherence regime, where the quantum discord is frozen to its initial value, while the classical correlation decays. After this time, the system is in quantum decoherence regime, where the classical correlation is frozen, while the quantum discord begins to decay to zero eventually. In this model, the non-Markovian takes no qualitative impact on the frozen behavior of quantum discord.
Secondly, we study the non-Markovian correlation dynamics of two initially quantum cor-related continuous-variable systems immersed in two independent dissipative noises. It is found that the non-Markovian effect makes partial of the initial quantum discord frozen to its long-time steady state, which is qualitatively different from the monotonic decay behavior under the Born-Markovian approximation. It indicates that the Born-Markovian appximation fails to capture the physics in this parameter regime. Further study reveals that such forever frozen of the quantum discord is caused by the formation of a localized mode between each system and its coupled environments. According to this mechanism, we give a quantitative criterion to judge the physical condition in the presence of the quantum-discord frozen behavior, which can give a useful guideline to experiment in suppressing the detrimental impacts of decoherence.
Thirdly, we study the correlation dynamics of two initially quantum dis-corrclated discrcte-variable systems with one of them immersed in a dissipative noise. It is found that the single local noise can not only induce transient quantum discord between the two systems, but also can make the induced quantum discord preserved in the long-time steady state. This is dramatically different from the previous results in the literature, where the transiently induced quantum discord decays to zero eventually. Our result reveals that we can generate steady quantum discord without resorting to interaction, neither direct interaction nor indirect interaction, and a single local dissipative noise can efficiently induce a steady quantum discord between the two systems. Further study shows that, same as the continuous-variable system, such steady quantum-discord generation is also dependent on the formation of a bound state between the system and its local noise. Our result indicates a new way to generate steady quantum discord for experiment without resorting to interaction but a local dissipative environment.
All of our studies reveal the profound impacts of the non-Markovian effect in quantum information processing and the distinctive difference between quantum discord and quantum entanglement in characterizing quantum correlation. The mechanism of the formation of a bound state or a coupled localized mode in suppressing decoherence supplies a new method to experiment in beating the decoherence in practise.
首先,我们研究了两个初始具有量子关联的分立变量系统在两个独立退相位噪声中的non-Markovian关联动力学。我们发现不同于量子纠缠渐进单调地趋于零的行为,系统的量子失协和经典关联在演化过程中存在一个从经典退相干到量子退相干的转变时刻,在该时刻之前,系统处在经典退相干区,此时退相位将使得量子失协在有限的时间内冻结在其初始值上,而经典关联发生衰减；在该时刻之后,系统处在量子退相干区,此时退相位将使得经典关联保持不变,而量子失协开始衰减并最终趋于零。在这个模型中,non-Markovian效应并没有对该量子关联演化行为带来定性的影响。
其次,我们研究了两个初始具有量子关联的连续变量系统在两个独立的耗散噪声中的non-Markovian关联动力学。我们发现：non-Markovian效应将使得初态中的量子失协部分地永久冻结在其长时稳态上,该结果与基于Born-Markovian近似下量子失协渐进地趋于零的结果具有定性的不同,说明此时Born-Markovian近似已不能描述系统的退相干行为；进一步的分析表明,量子失协的该持久冻结机制来源于各子系统与其环境形成一个耦合的局域化模式,根据此机制,我们给出了量子失协永久冻结的定量判据,该判据揭示出我们可以通过调控系统与环境的耦合以及环境的谱密度来对退相干进行抑制,为从实验上实现退相干的抑制提供了新的方法。
最后,我们研究了两个初始没有量子关联的分立变量系统,其中之一受到局域耗散噪声环境影响的关联动力学。我们发现：在non-Markovian动力学下,该耗散噪声不仅能够瞬时地诱导出量子系统之间的量子失协,而且能够使得该量子失协免受进一步的退相干影响以保持到其长时稳态,该结果与以前文献中基于Born-Markovian近似的该瞬时诱导出的量子失协渐进地趋于零的结果具有定性的不同；揭示了不诉诸于直接或间接相互作用,通过单个局域的耗散噪声来制备量子系统之间稳定量子失协的物理策略。分析表明：该稳定的量子失协制备同样决定于系统与其耦合环境束缚态形成的物理判据,我们所得到的解析判据为从实验上制备各子系统之间稳定的量子失协提供了理论依据。
我们的结果系统地展示了non-Markovian效应在具体量子信息处理中的显著作用,也反映了量子失协与量子纠缠在刻画量子关联中定性的不同；我们所发现的系统与环境束缚态／耦合局域模式的形成所导致的退相干抑制为实验上探索退相干控制方案提供了新的策略。
It is one of the crucial issues in quantum engineering field to evaluate the detrimental impacts of decoherence on the schemes of the single-quantum-state control and exploring its efficient suppression strategy. The rapid development of the experimental technique in this field also asks for the establishment of the general description to the decoherence going beyond the widely-used Born-Markovian approximation and the pursuit of the new physics induced by the non-Markovian effect in explicit physical systems. On the other hand, it is found that quantum entanglement cannot exhaust all the characters of quantum correlation, and quantum correlation can be characterized by the so-called quantum discord in a more general way than the quantum entanglement. Therefore, the study on exploring the quantitative or even qualitative difference between quantum discord and quantum entanglement in the protocols of quantum information processing is a hot topics in quantum information science recently. Motivated by these two aspects, we study in this thesis the non-Markovian correlation dynamics of the following several systems influenced by different type of decoherence channels:
Firstly, we study the non-Markovian correlation dynamics of two initially quantum corre-lated discrete-variable systems immersed in two independent dephasing noises. It is found that much different from the behavior of the monotonic decay to zero of quantum entanglement, the behavior of quantum discord and classical correlation shows a transition behavior at certain time from classical decoherence to quantum decoherence. Before this time, the system is in classical decoherence regime, where the quantum discord is frozen to its initial value, while the classical correlation decays. After this time, the system is in quantum decoherence regime, where the classical correlation is frozen, while the quantum discord begins to decay to zero eventually. In this model, the non-Markovian takes no qualitative impact on the frozen behavior of quantum discord.
Secondly, we study the non-Markovian correlation dynamics of two initially quantum cor-related continuous-variable systems immersed in two independent dissipative noises. It is found that the non-Markovian effect makes partial of the initial quantum discord frozen to its long-time steady state, which is qualitatively different from the monotonic decay behavior under the Born-Markovian approximation. It indicates that the Born-Markovian appximation fails to capture the physics in this parameter regime. Further study reveals that such forever frozen of the quantum discord is caused by the formation of a localized mode between each system and its coupled environments. According to this mechanism, we give a quantitative criterion to judge the physical condition in the presence of the quantum-discord frozen behavior, which can give a useful guideline to experiment in suppressing the detrimental impacts of decoherence.
Thirdly, we study the correlation dynamics of two initially quantum dis-corrclated discrcte-variable systems with one of them immersed in a dissipative noise. It is found that the single local noise can not only induce transient quantum discord between the two systems, but also can make the induced quantum discord preserved in the long-time steady state. This is dramatically different from the previous results in the literature, where the transiently induced quantum discord decays to zero eventually. Our result reveals that we can generate steady quantum discord without resorting to interaction, neither direct interaction nor indirect interaction, and a single local dissipative noise can efficiently induce a steady quantum discord between the two systems. Further study shows that, same as the continuous-variable system, such steady quantum-discord generation is also dependent on the formation of a bound state between the system and its local noise. Our result indicates a new way to generate steady quantum discord for experiment without resorting to interaction but a local dissipative environment.
All of our studies reveal the profound impacts of the non-Markovian effect in quantum information processing and the distinctive difference between quantum discord and quantum entanglement in characterizing quantum correlation. The mechanism of the formation of a bound state or a coupled localized mode in suppressing decoherence supplies a new method to experiment in beating the decoherence in practise.
引文
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