量子轨迹的暗子空间与不变测度
Dark Subspaces and Invariant Measures of Quantum Trajectories
AI总结：
本文研究了量子轨迹的不变测度，通过分析暗子空间上的马尔可夫过程并利用等距族最小性概念，建立了量子轨迹不变测度与遍历测度的完整分类。
摘要：
量子轨迹是描述受间接测量影响的量子系统演化的马尔可夫过程。它们可被视为依赖于位置的迭代函数系统，或是相依且非同分布随机矩阵乘积的结果。本文建立了其不变测度的完整分类。该分类分两步完成。首先，我们证明了在由（Maassen, Kümmerer 2006）定义的被称为暗子空间的某些线性子空间上，马尔可夫过程存在唯一的不变测度。其次，我们研究了暗子空间内部的过程。利用从参考空间到暗子空间的等距族最小性概念，我们证明了一组由酉群轨道索引的测度即为量子轨迹的遍历测度集。
英文摘要：
Quantum trajectories are Markov processes describing the evolution of a quantum system subject to indirect measurements. They can be viewed as place dependent iterated function systems or the result of products of dependent and non identically distributed random matrices. In this article, we establish a complete classification of their invariant measures. The classification is done in two steps. First, we prove a Markov process on some linear subspaces called dark subspaces, defined in (Maassen, Kümmerer 2006), admits a unique invariant measure. Second, we study the process inside the dark subspaces. Using a notion of minimal family of isometries from a reference space to dark subspaces, we prove a set of measures indexed by orbits of a unitary group is the set of ergodic measures of quantum trajectories.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
