量子关联动力学的理论研究
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摘要
量子信息与量子计算是涉及量子力学、信息科学和计算科学的一门交叉学科,其开端可追溯到上个世纪八十年代初。随后,量子算法、量子密码术与量子通讯等研究方向都取得了巨大的进展。值得强调的是,量子纠缠作为量子信息和量子计算中的重要资源和组成部分,业已吸引了众多物理学家的研究兴趣。曾经,量子纠缠被认为与量子关联相同,但现在越来越多的研究者认为量子纠缠仅是一种特殊的量子关联,并发现无纠缠的量子关联态仍能用来处理很多经典计算不能处理的问题。
量子计算需要利用量子态的相干性,但在量子信息处理过程中,量子系统不可避免地会受到退相干的影响,从而使得量子的相干性遭到破坏,甚至消失。对量子退相干的研究将有助于我们更好地实现量子计算。再者,量子关联的动力学是指量子关联的时间演化问题,对它进行研究能让我们更好地理解量子关联以及量子信息处理中存在的问题。因此本文重点研究不同退相干环境下的量子关联动力学。主要包括以下内容：
1.研究了自旋链环境下的量子关联动力学。其一,研究了与Ising自旋链相耦合的中心qubit-qubit的量子关联,其中量子关联用量子失协和几何的方法来度量。结果表明,在弱耦合时,量子失协和几何度量都能探测到Ising链的相变点。在相变点附近,演化过程会出现量子失协和经典关联的突变。另外,对某些初态,量子关联的几何度量会出现不随时间变化的现象。其二,进而考虑具有Dzyaloshinsky-Moriya(DM)相互作用的XY链,中心原子也设为qubit-qutrit系统,量子关联则用量子失协和测致扰动来度量。作为比较,同时也研究用来度量量子纠缠的负性演化。我们解析地计算出一类qubit-qutrit态的三种关联的演化形式。结果表明,以上三种关联中用量子失协来探测量子相变是最优的。且DM相互作用不改变XY链的相变点,但会加快量子关联的衰变。此外,当仅有qubit与自旋链耦合时,量子失协和经典关联之间会发生突变。在演化过程中,只有纠缠才会出现突然死亡。
2.研究了不同的噪声环境下qutrit-qutrit系统量子关联的演化。计算过程中,用几何度量来表征量子关联。退相干信道分别选择位相衰变信道和极化衰变信道。首先,研究了一类束缚纠缠态的量子关联动力学。结果表明,位相噪声影响下量子的关联衰变速率比极化噪声时快。第二,研究了一类特殊态的演化。计算显示,该初态的量子关联在接近束缚纠缠态和自由纠缠态的分界处发生突变。在单体和多体局域极化噪声下,该突变点保持不变。在初态参数某些区域,量子关联的演化与初态参数无关。而在位相噪声中,此种现象在局域作用下不会发生,但是在集体作用下会出现。第三,进而研究了对上述的态进行局域操作的影响。结果发现,在极化噪声环境下,量子关联不发生改变。但是在位相噪声下,量子关联的衰变会变慢。第四,研究了类Werner态的相关行为。结果表明,在集体位相噪声和局域极化噪声作用下,量子关联会趋向不同的定值。
Quantum information and quantum computation(QIQC) is an interdiscipline in-volving quantum mechanics, information and computation science, which can be traced back to the1980s. Considerable progress on quantum algorithm, quantum cryptography and quantum communication has been achieved since then. Notably, quantum entangle-ment, as an essential resource and ingredient of QIQC, has attracted much attention from physicists. It was considered that quantum correlation was exactly quantum entangle-ment, but more and more researchers now recognize that quantum entanglement is just one special kind of quantum correlations, and find that the unentangled state containing quantum correlation can be used to implement the tasks that classical computation fails to achieve.
Quantum computer is designed by employing the coherence of quantum state. However, due to decoherence, quantum coherence in quantum computation will in-evitably decrease, even vanish. The research on decoherence will contribute to imple-mentation in quantum computation. The dynamics of quantum correlation refers to the time evolution of quantum correlation, researches on which will provide a better un-derstanding of both quantum correlation and existing problems in quantum information processing. Therefore, in the thesis we mainly study the dynamics of quantum cor-relation under different decoherence environments. The main content of the paper is organized as follows:
1. We study the dynamics of correlation under the spin chain environment. Firstly, the dynamics of correlation for a central two-qubit system coupled to an Ising spin chain is investigated, where quantum correlation is quantified by both quantum discord and geometric measure of quantum discord(GMQD). It is found that the two measures can be used to detect the quantum phase transition point of Ising spin chain under the weak-coupling condition. There exists a sudden transition between quantum discord and clas-sical correlation near the phase transition point under the evolution. GMQD keeps un-changed for some initial states. Secondly, we consider the dynamics of correlations for a hybrid qubit-qutrit system in an XY spin-chain environment with Dzyaloshinsky-Moriya(DM) interaction. Quantum correlation is measured via quantum discord and measurement-induced disturbance(MID), respectively. In order to compare with the behaviors of quantum correlations, we also focus on the dynamics of entanglement, measured by negativity. The expressions of negativity, quantum discord and MID for a class of states can be calculated analytically, respectively. It is found that quantum discord is optimal among the three measures to detect the critical point of quantum phase transition. DM interaction does not affect QPT induced by the external magnetic field and only enhances the decay of quantum correlations. When only the qubit in-teracts with the environment, the phenomenon of sudden transition between classical correlation and quantum discord is observed. Entanglement suffers sudden death while quantum discord and MID decay asymptotically.
2. We study the dynamics of quantum correlation for qutrit-qutrit states under depolarizing and dephasing noise, in which GMQD is used to quantify quantum cor-relation. Firstly, the dynamics of quantum correlation for a family of bound-entangled states is investigated. The decay rate of quantum correlation under depolarizing noise is slower than that under dephasing. Secondly, quantum correlations for a class of particu-lar initial states exist a sudden change near the transition point from bound-entangled to free-entangled state. The sudden change point remains unchanged in the later evolution under local and multilocal depolarizing noise. The behavior of quantum correlations is independent of the parameter of given initial states in many regions. However, the phe-nomenon does not exist under local dephasing noise, and it only occurs under collective dephasing. Thirdly, it is found that local transformation for the previous states does not change the behavior of quantum correlations under depolarizing noise, but it slows the decay of quantum correlations. Finally, we investigate the dynamics of quantum corre-lations for the Werner-like state and find that quantum correlations tend to be different constants under collective dephasing and local depolarizing noise.
量子计算需要利用量子态的相干性,但在量子信息处理过程中,量子系统不可避免地会受到退相干的影响,从而使得量子的相干性遭到破坏,甚至消失。对量子退相干的研究将有助于我们更好地实现量子计算。再者,量子关联的动力学是指量子关联的时间演化问题,对它进行研究能让我们更好地理解量子关联以及量子信息处理中存在的问题。因此本文重点研究不同退相干环境下的量子关联动力学。主要包括以下内容：
1.研究了自旋链环境下的量子关联动力学。其一,研究了与Ising自旋链相耦合的中心qubit-qubit的量子关联,其中量子关联用量子失协和几何的方法来度量。结果表明,在弱耦合时,量子失协和几何度量都能探测到Ising链的相变点。在相变点附近,演化过程会出现量子失协和经典关联的突变。另外,对某些初态,量子关联的几何度量会出现不随时间变化的现象。其二,进而考虑具有Dzyaloshinsky-Moriya(DM)相互作用的XY链,中心原子也设为qubit-qutrit系统,量子关联则用量子失协和测致扰动来度量。作为比较,同时也研究用来度量量子纠缠的负性演化。我们解析地计算出一类qubit-qutrit态的三种关联的演化形式。结果表明,以上三种关联中用量子失协来探测量子相变是最优的。且DM相互作用不改变XY链的相变点,但会加快量子关联的衰变。此外,当仅有qubit与自旋链耦合时,量子失协和经典关联之间会发生突变。在演化过程中,只有纠缠才会出现突然死亡。
2.研究了不同的噪声环境下qutrit-qutrit系统量子关联的演化。计算过程中,用几何度量来表征量子关联。退相干信道分别选择位相衰变信道和极化衰变信道。首先,研究了一类束缚纠缠态的量子关联动力学。结果表明,位相噪声影响下量子的关联衰变速率比极化噪声时快。第二,研究了一类特殊态的演化。计算显示,该初态的量子关联在接近束缚纠缠态和自由纠缠态的分界处发生突变。在单体和多体局域极化噪声下,该突变点保持不变。在初态参数某些区域,量子关联的演化与初态参数无关。而在位相噪声中,此种现象在局域作用下不会发生,但是在集体作用下会出现。第三,进而研究了对上述的态进行局域操作的影响。结果发现,在极化噪声环境下,量子关联不发生改变。但是在位相噪声下,量子关联的衰变会变慢。第四,研究了类Werner态的相关行为。结果表明,在集体位相噪声和局域极化噪声作用下,量子关联会趋向不同的定值。
Quantum information and quantum computation(QIQC) is an interdiscipline in-volving quantum mechanics, information and computation science, which can be traced back to the1980s. Considerable progress on quantum algorithm, quantum cryptography and quantum communication has been achieved since then. Notably, quantum entangle-ment, as an essential resource and ingredient of QIQC, has attracted much attention from physicists. It was considered that quantum correlation was exactly quantum entangle-ment, but more and more researchers now recognize that quantum entanglement is just one special kind of quantum correlations, and find that the unentangled state containing quantum correlation can be used to implement the tasks that classical computation fails to achieve.
Quantum computer is designed by employing the coherence of quantum state. However, due to decoherence, quantum coherence in quantum computation will in-evitably decrease, even vanish. The research on decoherence will contribute to imple-mentation in quantum computation. The dynamics of quantum correlation refers to the time evolution of quantum correlation, researches on which will provide a better un-derstanding of both quantum correlation and existing problems in quantum information processing. Therefore, in the thesis we mainly study the dynamics of quantum cor-relation under different decoherence environments. The main content of the paper is organized as follows:
1. We study the dynamics of correlation under the spin chain environment. Firstly, the dynamics of correlation for a central two-qubit system coupled to an Ising spin chain is investigated, where quantum correlation is quantified by both quantum discord and geometric measure of quantum discord(GMQD). It is found that the two measures can be used to detect the quantum phase transition point of Ising spin chain under the weak-coupling condition. There exists a sudden transition between quantum discord and clas-sical correlation near the phase transition point under the evolution. GMQD keeps un-changed for some initial states. Secondly, we consider the dynamics of correlations for a hybrid qubit-qutrit system in an XY spin-chain environment with Dzyaloshinsky-Moriya(DM) interaction. Quantum correlation is measured via quantum discord and measurement-induced disturbance(MID), respectively. In order to compare with the behaviors of quantum correlations, we also focus on the dynamics of entanglement, measured by negativity. The expressions of negativity, quantum discord and MID for a class of states can be calculated analytically, respectively. It is found that quantum discord is optimal among the three measures to detect the critical point of quantum phase transition. DM interaction does not affect QPT induced by the external magnetic field and only enhances the decay of quantum correlations. When only the qubit in-teracts with the environment, the phenomenon of sudden transition between classical correlation and quantum discord is observed. Entanglement suffers sudden death while quantum discord and MID decay asymptotically.
2. We study the dynamics of quantum correlation for qutrit-qutrit states under depolarizing and dephasing noise, in which GMQD is used to quantify quantum cor-relation. Firstly, the dynamics of quantum correlation for a family of bound-entangled states is investigated. The decay rate of quantum correlation under depolarizing noise is slower than that under dephasing. Secondly, quantum correlations for a class of particu-lar initial states exist a sudden change near the transition point from bound-entangled to free-entangled state. The sudden change point remains unchanged in the later evolution under local and multilocal depolarizing noise. The behavior of quantum correlations is independent of the parameter of given initial states in many regions. However, the phe-nomenon does not exist under local dephasing noise, and it only occurs under collective dephasing. Thirdly, it is found that local transformation for the previous states does not change the behavior of quantum correlations under depolarizing noise, but it slows the decay of quantum correlations. Finally, we investigate the dynamics of quantum corre-lations for the Werner-like state and find that quantum correlations tend to be different constants under collective dephasing and local depolarizing noise.
引文
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