Infinite dimensional dynamical maps

TL;DR

This paper investigates the properties of infinite dimensional quantum dynamical maps, providing conditions for their divisibility and exploring specific cases like Gaussian maps, thereby extending the understanding of quantum Markovianity beyond finite dimensions.

Contribution

It introduces sufficient conditions for P and CP divisibility of infinite dimensional dynamical maps and applies these to Gaussian maps, expanding the theoretical framework in quantum information.

Findings

Established criteria for divisibility of infinite dimensional dynamical maps

Constructed examples of infinite dimensional dynamical maps

Extended results to Gaussian dynamical maps

Abstract

Completely positive trace preserving maps are widely used in quantum information theory. These are mostly studied using the master equation perspective. A central part in this theory is to study whether a given system of dynamical maps $\{\Lambda_t: t \ge 0\}$ is Markovian or non-Markovian. We study the problem when the underlying Hilbert space is of infinite dimensional. We construct a sufficient condition for checking P (resp. CP) divisibility of dynamical maps. We construct several examples where the underlying Hilbert space may not be of finite dimensional. We also give a special emphasis on Gaussian dynamical maps and get a version of our result in it.