论文标题
量子状态平滑的一般标准，具有线性高斯量子系统的必要和足够标准
General criteria for quantum state smoothing with necessary and sufficient criteria for linear Gaussian quantum systems
论文作者
论文摘要
量子状态平滑是一种在时间$τ$下估算部分观察到的量子系统的量子状态的技术，以整个观察到的测量记录（无论是在$τ$之前还是之后）。但是，这种平滑技术需要一个观察者（Alice，say）知道她未知的测量记录的性质，以表征Bob（例如）系统的可能的真实状态。如果爱丽丝对鲍勃系统的真实状态做出了不正确的假设，那么她将获得一个次优的平滑状态，更糟糕的是，可能是无法实现的（不对对应于真实状态的有效进化），甚至是无形的（未由状态矩阵$ρ\ egeq0 $表示）。在本文中，我们回顾量子状态平滑的历史背景，并列出一般标准应满足平滑量子状态。然后，对于线性高斯量子系统的情况，我们得出了对真实状态的协方差矩阵的实现性的必要且足够的约束。自然，真实状态的可实现协方差保证了身体平滑的状态。可以认为，任何假定的真实协方差赋予物理平滑状态都是可实现的真实协方差，但我们明确地表明并非如此。这强调了Realizabilty约束的重要性。
Quantum state smoothing is a technique for estimating the quantum state of a partially observed quantum system at time $τ$, conditioned on an entire observed measurement record (both before and after $τ$). However, this smoothing technique requires an observer (Alice, say) to know the nature of the measurement records that are unknown to her in order to characterize the possible true states for Bob's (say) systems. If Alice makes an incorrect assumption about the set of true states for Bob's system, she will obtain a smoothed state that is suboptimal, and, worse, may be unrealizable (not corresponding to a valid evolution for the true states) or even unphysical (not represented by a state matrix $ρ\geq0$). In this paper, we review the historical background to quantum state smoothing, and list general criteria a smoothed quantum state should satisfy. Then we derive, for the case of linear Gaussian quantum systems, a necessary and sufficient constraint for realizability on the covariance matrix of the true state. Naturally, a realizable covariance of the true state guarantees a smoothed state which is physical. It might be thought that any putative true covariance which gives a physical smoothed state would be a realizable true covariance, but we show explicitly that this is not so. This underlines the importance of the realizabilty constraint.
