On the universal constraints for relaxation rates for quantum dynamical semigroup

TL;DR

This paper proposes a conjecture on universal constraints for relaxation rates in quantum dynamical semigroups, supported by theoretical analysis and numerical evidence, with implications for quantum channel spectra and Markovianity.

Contribution

It introduces a new conjecture on relaxation rate constraints that applies to various quantum semigroups and has significant implications for quantum channel analysis.

Findings

The conjecture holds for unital semigroups.

It is valid for semigroups from microscopic models in the weak coupling limit.

Numerical analysis supports the conjecture's validity.

Abstract

A conjecture for the universal constraints for relaxation rates of a quantum dynamical semigroup is proposed. It is shown that it holds for several interesting classes of semigroups, e.g. unital semigroups and semigroups derived in the weak coupling limit from the proper microscopic model. Moreover, proposed conjecture is supported by numerical analysis. This conjecture has several important implications: it allows to provide universal constraints for spectra of quantum channels and provides necessary condition to decide whether a given channel is consistent with Markovian evolution.