Invertibility as a witness of Markovianity of the quantum dynamical maps

TL;DR

This paper identifies a class of quantum dynamical maps where invertibility is essential for Markovianity, enabling straightforward non-Markovianity detection through quantum-state tomography without optimization.

Contribution

It introduces a class of quantum processes where invertibility is necessary for Markovianity, clarifying the relations between divisibility, invertibility, and Markovianity.

Findings

Invertibility is necessary for Markovianity in the identified class.

Quantum-state tomography can determine non-Markovianity without optimization.

Relations between divisibility, invertibility, and Markovianity vary outside the class.

Abstract

Markovianity of the quantum open system processes is a topic of the considerable current interest. Typically, invertibility is assumed to be non-essential for Markovianity of the open-quantum-system dynamical maps. Nevertheless, in this paper we distinguish a class of physically important dynamical maps (processes) for which invertibility is a necessary condition for Markovianity. Since every quantum-state tomography directly provides information on invertibility of the map, no optimization procedure is necessary for determining non-Markovianity regarding the considered class of dynamical processes. On this basis we are able to provide a systematic insight and to distinguish mutual relations of the various approaches to quantum Markovianity. Notably, for the processes out of the considered class of dynamical maps, various relations are allowed between divisibility, invertibility and Markovianity of the dynamical maps.