Contiguity of States and Super Wave Operators

Abstract

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.