开放量子系统协方差矩阵的相干跟踪
Coherently tracking the covariance matrix of an open quantum system
摘要：
量子系统的相干反馈控制比基于测量的控制具有明显的优势，但到目前为止，在相干估计器和更具体的相干观测器上做的工作很少。相干观测器的输入是一个特定的量子植物的相干输出，并且被设计成使得观测器的某些子集和植物的期望值收敛于渐近极限。我们以前开发了一类平均跟踪（MT）观测器的开放谐振子，只收敛于平均位置和动量;在这里，我们开发了一类协方差矩阵跟踪（CMT）相干观测器，跟踪量子植物的平均和协方差矩阵。我们得到了CMT观测器存在的充分必要条件，并发现CMT观测器比MT观测器有更多的限制。我们给出的例子，我们演示了如何设计一个CMT观察员，并显示它可以用来跟踪像纠缠的植物属性。由于CMT观测器比MT观测器提供更多的量子信息，我们期望它在未来的相干反馈方案中有更大的应用。对相干量子估计器和观测器的研究在量子测量的讨论中是很重要的，因为它们提供了对系统量子态的估计，而在它们的推导中没有明确使用测量假设。
英文摘要：
Coherent feedback control of quantum systems has demonstrable advantages over measurement-based control, but so far there has been little work done on coherent estimators and more specifically coherent observers. Coherent observers are input the coherent output of a specified quantum plant, and are designed such that some subset of the observer and plant's expectation values converge in the asymptotic limit. We previously developed a class of mean tracking (MT) observers for open harmonic oscillators that only converged in mean position and momentum; Here we develop a class of covariance matrix tracking (CMT) coherent observers that track both the mean and covariance matrix of a quantum plant. We derive necessary and sufficient conditions for the existence of a CMT observer, and find there are more restrictions on a CMT observer than there are on a MT observer. We give examples where we demonstrate how to design a CMT observer and show it can be used to track properties like the entanglement of a plant. As the CMT observer provides more quantum information than a MT observer, we expect it will have greater application in future coherent feedback schemes mediated by coherent observers. Investigation of coherent quantum estimators and observers is important in the ongoing discussion of quantum measurement; As they provide estimation of a system's quantum state without explicit use of the measurement postulate in their derivation.
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