Quantum regression in dephasing phenomena

TL;DR

This paper examines the conditions under which quantum regression holds in phase-damping dynamics, focusing on dephasing phenomena and specific spin-boson models to identify when quantum regression is valid.

Contribution

It provides necessary and sufficient conditions for quantum regression validity in dephasing systems and explores specific models ensuring its exact applicability.

Findings

Necessary conditions for nontrivial dephasing compatible with quantum regression

Hierarchy of equations equivalent to quantum regression validity

Identification of coupling functions in spin-boson models that preserve quantum regression

Abstract

We investigate the validity of quantum regression for a family of quantum Hamiltonians on a multipartite system leading to phase-damping reduced dynamics. After finding necessary and sufficient conditions for the CP-divisibility of the corresponding channel, we evaluate a hierarchy of equations equivalent to the validity of quantum regression under arbitrary interventions; in particular, we find necessary conditions for a nontrivial dephasing to be compatible with quantum regression. In this framework, we study a class of dephasing-type generalized spin-boson (GSB) models, investigating the existence of qubit-environment coupling functions that ensure the exact validity of quantum regression.