New Approaches to Honesty Theory and Applications in Quantum Dynamical Semigroups

TL;DR

This paper introduces new characterizations of honesty in quantum dynamical semigroups using three approaches, linking honesty to conservativity and expanding the theoretical framework of quantum state evolution.

Contribution

It provides novel characterizations of honesty in perturbed semigroups and applies these results to quantum dynamical semigroups, broadening the understanding of their properties.

Findings

Honesty is a natural extension of conservativity.

New characterizations of honesty via mean ergodicity, adjoint operators, and uniqueness.

Application of honesty theory to quantum dynamical semigroups.

Abstract

We prove some new characterisations of honesty of the perturbed semigroup in Kato's Perturbation Theorem on abstract state spaces via three approaches, namely mean ergodicity of operators, adjoint operators and uniqueness of the perturbed semigroup. We then apply Kato's Theorem on abstract state spaces and the honesty theory linked to it to the study of quantum dynamical semigroups. We show that honesty is the natural generalisation of the notion of conservativity.