Efficient and operational quantifier of non-divisibility in terms of channel discrimination

TL;DR

This paper introduces an efficient method using semidefinite programming to detect and quantify non-divisibility in quantum channels, aiding the understanding of quantum dynamics and non-Markovian behavior.

Contribution

It presents a novel operational approach to measure non-divisibility of quantum channels via channel discrimination, extending the tools for analyzing quantum dynamics.

Findings

Efficient semidefinite programming method for channel discrimination.

Quantitative measure of non-divisibility in quantum channels.

Operational framework for analyzing quantum non-Markovianity.

Abstract

The understanding of open quantum systems is crucial for the development of quantum technologies. Of particular relevance is the characterisation of divisible quantum dynamics, seen as a generalisation of Markovian processes to the quantum setting. Here, we propose a way to detect divisibility and quantify how non-divisible a quantum channel is through the concept of channel discrimination. We ask how well we can distinguish generic dynamics from divisible dynamics. We show that this question can be answered efficiently through semidefinite programming, which provides us with an operational and efficient way to quantify divisibility.