标题： 展开量子动力学中的规范自由度：不同的连续测量何时会产生相同的量子轨迹？ 显示英文标题

标题： Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories?

摘要： 马尔可夫开放量子系统的量子轨迹来源于对系统相互作用的环境进行测量所产生的反作用。 在本工作中，我们考虑量子跃迁的计数测量，这些测量对应于同一量子主方程的不同表示形式。 我们推导出在何种条件下这些不同的测量会产生相同的未展开量子主方程，该方程描述了系统纯条件态概率分布的动力学。 由于该方程唯一地决定了条件态的随机动力学，我们还得到了不同测量导致相同量子轨迹的必要且充分条件。 随后，我们考虑条件态和测量记录的联合随机动力学。 我们以标记的量子轨迹来表述这一点，并推导出在何种条件下不同的表示会导致等价的标记量子轨迹，最多仅相差标签的排列。 由于这些条件通常更严格，我们最后构造了粗粒度的测量记录，使得相应部分标记轨迹的等价性由轨迹本身的等价性保证。 这些一般结果通过两个例子加以说明，这两个例子展示了标签的排列以及不同量子轨迹的等价性。 显示英文摘要

摘要： Quantum trajectories of a Markovian open quantum system arise from the back-action of measurements performed in the environment with which the system interacts. In this work, we consider counting measurements of quantum jumps, corresponding to different representations of the same quantum master equation. We derive necessary and sufficient conditions under which these different measurements give rise to the same unravelled quantum master equation, which governs the dynamics of the probability distribution over pure conditional states of the system. Since that equation uniquely determines the stochastic dynamics of a conditional state, we also obtain necessary and sufficient conditions under which different measurements result in identical quantum trajectories. We then consider the joint stochastic dynamics for the conditional state and the measurement record. We formulate this in terms of labelled quantum trajectories, and derive necessary and sufficient conditions under which different representations lead to equivalent labelled quantum trajectories, up to permutations of labels. As those conditions are generally stricter, we finish by constructing coarse-grained measurement records, such that equivalence of the corresponding partially-labelled trajectories is guaranteed by equivalence of the trajectories alone. These general results are illustrated by two examples that demonstrate permutation of labels, and equivalence of different quantum trajectories.