Non-Markovianity of Gaussian Channels

TL;DR

This paper presents a precise criterion for identifying non-Markovian behavior in Gaussian quantum channels, based on divisibility violations, without relying on traditional state optimization methods.

Contribution

It introduces a novel, necessary and sufficient divisibility-based criterion for non-Markovianity in Gaussian channels, avoiding the Choi-Jamiolkowski approach.

Findings

Provides a clear mathematical condition for non-Markovianity

Eliminates the need for state optimization in analysis

Offers a practical tool for quantum channel characterization

Abstract

We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated to arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.