Stochastic Isometries in Quantum Mechanics

TL;DR

This paper characterizes stochastic isometries in quantum mechanics, which are special linear maps preserving trace and positivity, and discusses their potential physical applications.

Contribution

It provides a mathematical characterization of stochastic isometries and explores their relevance in representing reversible quantum dynamics and symmetries.

Findings

Characterization of stochastic isometries as trace-preserving, positive, linear maps.

Identification of physical contexts where stochastic isometries are applicable.

Insights into the structure of reversible quantum transformations.

Abstract

The class of stochastic maps, that is, linear, trace-preserving, positive maps between the self-adjoint trace class operators of complex separable Hilbert spaces plays an important role in the representation of reversible dynamics and symmetry transformations. Here a characterization of the isometric stochastic maps is given and possible physical applications are indicated.