基于微波调控技术的量子非局域关联研究
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摘要
量子非局域性和量子关联是量子力学的两个独特的性质。作为两种不同的量子资源,在量子信息处理中扮演者十分重要的作用。到目前为止,在实验上已经利用纠缠光子对、原子的纠缠、囚禁离子的纠缠、原子与光子之间的纠缠、单个中子不同自由度之间的纠缠以及超导量子比特的纠缠等验证了量子非局域性(Bell不等式和无不等式形式的Hardy非局域性)。量子关联被认为是量子力学中一个比量子纠缠更基本的概念。量子关联是近年来的一个研究热点,吸引了很多研究者的兴趣。然而,在实际的条件下,量子系统不可避免的与周围的环境发生相互作用。这将导致量子系统发生退相干。因此,研究在退相干环境中量子关联的动力学是十分必要的。本文我们研究了在驱动腔系统(如电路量子电动力学系统)中基于量子非破坏性测量验证两体和三体量子非局域性以及在局域的退相干信道中两体量子态的量子关联的动力学。主要的研究内容如下：
1.在驱动腔系统中,当二能级原子(量子比特)色散耦合于腔场且考虑原子与腔场之间所有的统计量子关联(即超越了平均场近似),通过探测驱动腔的稳态透射谱可以实现对腔内两个二能级原子的量子非破坏性测量,即透射谱中每一个透射峰标记相应的计算基态且透射峰的相对高度等于相应的计算基态在被探测态中的叠加几率。基于这类量子非破坏性测量,不需要惯常的量子态层析技术就可以确定制备的量子态的存在。利用这类测量可以确定局域的经典变量之间的非局域关联函数。因此,表征两体量子非局域性的Bell不等式和梯子型Hardy非局域性可以被有效地验证。
2.作为两体量子非局域性验证的自然推广,基于驱动腔系统中三个二能级原子的量子非破坏性测量,对三种三比特量子态(GHZ态、W态和两体可分的三比特态),我们提出了验证三体量子非局域性(Mermin不等式和Svetlichny不等式)的实验上可行的方案。研究结果表明Mermin不等式可以被这三种量子态违背,但Svetlichny不等式只会被GHZ和W态违背。这意味着只有Svetlichny不等式才能表征真正的三体量子非局域性。因此,Svetlichny不等式的违背可以看作真正的三体纠缠存在的鲁棒的判据。
3.研究了在三类局域的退相干信道(比特翻转、相位翻转和比特-相位翻转信道)中一类两比特量子态的几何量子关联的动力学。我们发现,在退相干信道中这类态的几何量子关联存在四种动力学行为：单调地衰减到零；单调衰减过程中存在一个突变点；单调衰减过程中存在两个突变点；先在有限的时间内保持不变然后再单调地衰减到零。同时可以发现没有几何量子关联的突然死亡发生。进一步地,建立了在这三类退相干信道中几何量子关联的演化所满足的因式分解定律。一旦给定了退相干信道的类型,不需要借助于初态本身,从这个定律可得几何量子关联演化的下界。
4.研究了在五类局域的退相干信道(退相、相位翻转、bit/trit翻转、bit/trit相位翻转和退极化信道)中一类含有两个参数的qubit-qutrit态的经典关联、测量诱导扰动量化的量子关联和量子纠缠的动力学。我们发现,在一定条件下,经典关联保持不变或单调地衰减到零。测量诱导扰动存在三种动力学行为：单调地衰减到零；单调地衰减到一个非零的稳定值(即剩余量子关联存在)；先从零单调地增加到最大值再单调地减小到零。与量子纠缠的突然死亡现象不同,经典关联和测量诱导扰动都不会出现突然死亡。以非惯性系框架下的情况为例,我们研究了由Unruh效应产生的一类qubit-qutrit态的测量诱导扰动及其在这五类局域的退相干信道中的动力学。我们发现,随着加速参数的增加测量诱导扰动而减小。在退相干信道中这类态的测量诱导扰动单调地衰减到零或者一个非零的稳定值。对相同的退相干参数,随着加速参数的增加测量诱导扰动而减小
Quantum nonlocality and quantum correlation are two unique properties of quantum mechanics. As different kinds of quantum resources, they play important roles in quantum information processing. Up to now, quantum nonlocality characterized by Bell inequality and Hardy's nonlocality without inequality has been experimentally tested with the entanglement of photons, atoms, trapped ions, an atom and a photon, two degrees of freedom of single neutron, superconducting qubits, etc. Quantum correlation is considered as a more fundamental concept than quantum entanglement in quantum mechanics. In recent years, many researchers focus their attentions on this hot research topic. However, in a realistic condition, a quantum system would inevitably interact with its surrounding environments. This leads to decoherence of this system occurs. Thus it is necessary to study the dynamics of quantum correlation under decoherence. In this dissertation, we study how to test bipartite and tripartite quantum nonlocality in a driven cavity (eg. circuit QED system) based on quantum nondemolition measurements (QNDs) and the dynamics of quantum correlation under local decoherence channels. The major results are listed as follows:
1. For two two-level atoms (qubits) dispersively coupled to a driven cavity and considering all the statistical quantum correlations between atoms and cavity (i.e., beyond the mean-field approximation), the QND measurement of two two-level atoms can be realized by detecting steady-state transmission spectra of the driven cavity. Specifically, each peak in the transmission spectra marks one of the computational basis states and the relevant height of such a peak corresponds to the superposed probability of computational basis states in the detected states. With this kind of QND measurements, the generated Bell states can be robustly confirmed without conventional quantum state tomography. Further, the nonlocal correlation functions between local classical variables can be determined by QND measurements. In this way, bipartite quantum nonlocality characterized by Bell inequality and ladder-like Hardy's nonlocality can be efficiently tested.
2. As a natural generalization of the test of bipartite quantum nonlocality, based on the QND measurements of three two-level atoms in a driven cavity, we propose an experimentally feasible proposal to test tripartite quantum nonlocality characterized by Mermin inequality and Svetlichny inequality, for three kinds of three-qubit GHZ, W and biseparable states. It can be found that Mermin inequality can be violated for these three kinds of three-qubit states, while Svetlichny inequality can only be violated by GHZ and W states. This implies that only Svetlichny inequality can characterize genuine tripartite quantum nonlocality. Thus, the violation of Svetlichny inequality can be considered as a robust criterion of the existence of genuine tripartite quantum entanglement.
3. The dynamics of geometric measure of quantum discord (GMQD) for a class of two-qubit states under local decoherence channels (bit flip, phase flip and bit-phase flip) is investigated. It can be found that four kinds of dynamical behaviors of the GMQD under decoherence channels exist:monotonic decay to zero; existing a sudden change point during the monotonic decay; existing two sudden change points during the monotonic decay; first keeping unchanged in a finite interval and then monotonic decay to zero. Meanwhile, it can be also found that no sudden death of the GMQD occurs. Furthermore, a relevant factorization law concerning the evolution of the GMQD under decoherence channels is established. From this law, once the decoherence channels are given, the lower bound of GMQD can be obtained, without resorting to the initial quantum state itself.
4. We investigate the dynamics of classical correlation, quantum correlation quantified by measurement-induced disturbance (MID) and quantum entanglement for a class of two-parameter qubit-qutrit states under local decoherence channels (dephasing, phase flip, bit/trit flip, bit/trit phase flip and depolarizing). It can be seen that, under certain conditions, classical correlation may be keep unchanged or decay monotonically. MID shows three kinds of dynamical behaviors:monotonic decay to zero; monotonic decay to a nonzero steady value (i.e., residual quantum correlation exists); first increasing from zero to a maximal value and then decay to zero in a monotonic way. Different from the sudden death of quantum entanglement, no sudden death of classical and quantum correlations occurs. Taking the cases in noninertial frames as an example, we study the MID and its dynamics for a class of qubit-qutrit states generated by Unruh effect under these five kinds of local decoherence channels. It can be found that the MID decreases as the acceleration parameter increases. The MID under local decoherence channels can monotonically decay to zero or a nonzero steady value. For the same decoherence parameter, the MID decreases as the acceleration parameter increases.
1.在驱动腔系统中,当二能级原子(量子比特)色散耦合于腔场且考虑原子与腔场之间所有的统计量子关联(即超越了平均场近似),通过探测驱动腔的稳态透射谱可以实现对腔内两个二能级原子的量子非破坏性测量,即透射谱中每一个透射峰标记相应的计算基态且透射峰的相对高度等于相应的计算基态在被探测态中的叠加几率。基于这类量子非破坏性测量,不需要惯常的量子态层析技术就可以确定制备的量子态的存在。利用这类测量可以确定局域的经典变量之间的非局域关联函数。因此,表征两体量子非局域性的Bell不等式和梯子型Hardy非局域性可以被有效地验证。
2.作为两体量子非局域性验证的自然推广,基于驱动腔系统中三个二能级原子的量子非破坏性测量,对三种三比特量子态(GHZ态、W态和两体可分的三比特态),我们提出了验证三体量子非局域性(Mermin不等式和Svetlichny不等式)的实验上可行的方案。研究结果表明Mermin不等式可以被这三种量子态违背,但Svetlichny不等式只会被GHZ和W态违背。这意味着只有Svetlichny不等式才能表征真正的三体量子非局域性。因此,Svetlichny不等式的违背可以看作真正的三体纠缠存在的鲁棒的判据。
3.研究了在三类局域的退相干信道(比特翻转、相位翻转和比特-相位翻转信道)中一类两比特量子态的几何量子关联的动力学。我们发现,在退相干信道中这类态的几何量子关联存在四种动力学行为：单调地衰减到零；单调衰减过程中存在一个突变点；单调衰减过程中存在两个突变点；先在有限的时间内保持不变然后再单调地衰减到零。同时可以发现没有几何量子关联的突然死亡发生。进一步地,建立了在这三类退相干信道中几何量子关联的演化所满足的因式分解定律。一旦给定了退相干信道的类型,不需要借助于初态本身,从这个定律可得几何量子关联演化的下界。
4.研究了在五类局域的退相干信道(退相、相位翻转、bit/trit翻转、bit/trit相位翻转和退极化信道)中一类含有两个参数的qubit-qutrit态的经典关联、测量诱导扰动量化的量子关联和量子纠缠的动力学。我们发现,在一定条件下,经典关联保持不变或单调地衰减到零。测量诱导扰动存在三种动力学行为：单调地衰减到零；单调地衰减到一个非零的稳定值(即剩余量子关联存在)；先从零单调地增加到最大值再单调地减小到零。与量子纠缠的突然死亡现象不同,经典关联和测量诱导扰动都不会出现突然死亡。以非惯性系框架下的情况为例,我们研究了由Unruh效应产生的一类qubit-qutrit态的测量诱导扰动及其在这五类局域的退相干信道中的动力学。我们发现,随着加速参数的增加测量诱导扰动而减小。在退相干信道中这类态的测量诱导扰动单调地衰减到零或者一个非零的稳定值。对相同的退相干参数,随着加速参数的增加测量诱导扰动而减小
Quantum nonlocality and quantum correlation are two unique properties of quantum mechanics. As different kinds of quantum resources, they play important roles in quantum information processing. Up to now, quantum nonlocality characterized by Bell inequality and Hardy's nonlocality without inequality has been experimentally tested with the entanglement of photons, atoms, trapped ions, an atom and a photon, two degrees of freedom of single neutron, superconducting qubits, etc. Quantum correlation is considered as a more fundamental concept than quantum entanglement in quantum mechanics. In recent years, many researchers focus their attentions on this hot research topic. However, in a realistic condition, a quantum system would inevitably interact with its surrounding environments. This leads to decoherence of this system occurs. Thus it is necessary to study the dynamics of quantum correlation under decoherence. In this dissertation, we study how to test bipartite and tripartite quantum nonlocality in a driven cavity (eg. circuit QED system) based on quantum nondemolition measurements (QNDs) and the dynamics of quantum correlation under local decoherence channels. The major results are listed as follows:
1. For two two-level atoms (qubits) dispersively coupled to a driven cavity and considering all the statistical quantum correlations between atoms and cavity (i.e., beyond the mean-field approximation), the QND measurement of two two-level atoms can be realized by detecting steady-state transmission spectra of the driven cavity. Specifically, each peak in the transmission spectra marks one of the computational basis states and the relevant height of such a peak corresponds to the superposed probability of computational basis states in the detected states. With this kind of QND measurements, the generated Bell states can be robustly confirmed without conventional quantum state tomography. Further, the nonlocal correlation functions between local classical variables can be determined by QND measurements. In this way, bipartite quantum nonlocality characterized by Bell inequality and ladder-like Hardy's nonlocality can be efficiently tested.
2. As a natural generalization of the test of bipartite quantum nonlocality, based on the QND measurements of three two-level atoms in a driven cavity, we propose an experimentally feasible proposal to test tripartite quantum nonlocality characterized by Mermin inequality and Svetlichny inequality, for three kinds of three-qubit GHZ, W and biseparable states. It can be found that Mermin inequality can be violated for these three kinds of three-qubit states, while Svetlichny inequality can only be violated by GHZ and W states. This implies that only Svetlichny inequality can characterize genuine tripartite quantum nonlocality. Thus, the violation of Svetlichny inequality can be considered as a robust criterion of the existence of genuine tripartite quantum entanglement.
3. The dynamics of geometric measure of quantum discord (GMQD) for a class of two-qubit states under local decoherence channels (bit flip, phase flip and bit-phase flip) is investigated. It can be found that four kinds of dynamical behaviors of the GMQD under decoherence channels exist:monotonic decay to zero; existing a sudden change point during the monotonic decay; existing two sudden change points during the monotonic decay; first keeping unchanged in a finite interval and then monotonic decay to zero. Meanwhile, it can be also found that no sudden death of the GMQD occurs. Furthermore, a relevant factorization law concerning the evolution of the GMQD under decoherence channels is established. From this law, once the decoherence channels are given, the lower bound of GMQD can be obtained, without resorting to the initial quantum state itself.
4. We investigate the dynamics of classical correlation, quantum correlation quantified by measurement-induced disturbance (MID) and quantum entanglement for a class of two-parameter qubit-qutrit states under local decoherence channels (dephasing, phase flip, bit/trit flip, bit/trit phase flip and depolarizing). It can be seen that, under certain conditions, classical correlation may be keep unchanged or decay monotonically. MID shows three kinds of dynamical behaviors:monotonic decay to zero; monotonic decay to a nonzero steady value (i.e., residual quantum correlation exists); first increasing from zero to a maximal value and then decay to zero in a monotonic way. Different from the sudden death of quantum entanglement, no sudden death of classical and quantum correlations occurs. Taking the cases in noninertial frames as an example, we study the MID and its dynamics for a class of qubit-qutrit states generated by Unruh effect under these five kinds of local decoherence channels. It can be found that the MID decreases as the acceleration parameter increases. The MID under local decoherence channels can monotonically decay to zero or a nonzero steady value. For the same decoherence parameter, the MID decreases as the acceleration parameter increases.
引文
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