Noninvertibility and non-Markovianity of quantum dynamical maps

TL;DR

This paper investigates the causes and implications of noninvertibility and non-Markovianity in quantum dynamical maps, analyzing their properties, classifications, and the effects of mixing noninvertible maps.

Contribution

It identifies two types of noninvertibilities in quantum maps, explores their relation to Markovianity, and examines criteria for semigroup limits in parameterized map families.

Findings

Two broad types of noninvertibility are identified.

Mixing noninvertible maps can produce Markovian or non-Markovian maps.

Criteria for semigroup limits are discussed.

Abstract

We identify two broad types of noninvertibilities in quantum dynamical maps, one necessarily associated with CP indivisibility and one not so. We study the production of (non-)Markovian, invertible maps by the process of mixing noninvertible Pauli maps, and quantify the fraction of the same. The memory kernel perspective appears to be less transparent on the issue of invertibility than the approaches based on maps or master equations. Here we consider a related and potentially helpful issue: the identification of criteria of parameterized families of maps leading to the existence of a well-defined semigroup limit.