This paper characterises contiguity for families of states defined on a von Neumann algebra. It extends earlier research of my own published in [1], motivated by scattering theory and the celebrated work of Lucien Le Cam in classical probability. It is well-known that Le Cam did a major contribution to develop asymptotic methods in statistical decision theory, defining various new concepts, among them, contiguity of probability measures. In particular, contiguity of quantum states allows to explore different aspects of the large time behaviour of noncommutative Markov semigroups, among them, the super wave operator characterisation. I illustrate these results via quantum and classical examples of evolutions.

中文翻译：

---

状态的连续性和超波算子

本文描述了在冯诺依曼代数上定义的状态族的邻接性。它扩展了我自己在 [1] 中发表的早期研究，其动机是散射理论和 Lucien Le Cam 在经典概率方面的著名工作。众所周知，Le Cam 对发展统计决策理论中的渐近方法做出了重大贡献，定义了各种新概念，其中包括概率测度的连续性。特别是，量子态的连续性允许探索非交换马尔可夫半群的大时间行为的不同方面，其中包括超波算子表征。我通过进化的量子和经典例子来说明这些结果。