Detecting and quantifying non-Markovianity via quantum direct cause

TL;DR

This paper compares different witnesses of non-Markovianity in quantum processes, showing that some can detect non-Markovianity where others fail, and introduces a method to quantify quantum memory using pseudo-density matrices.

Contribution

It demonstrates the effectiveness of pseudo-density matrix-based measures in detecting and quantifying non-Markovianity, especially eternal non-Markovianity, and clarifies distinctions between weak and strong quantum direct cause.

Findings

Pseudo-density matrix measures can detect non-Markovianity missed by trace distance.

These measures can quantify total quantum memory in indivisible processes.

Temporal steerable correlations may not detect eternal non-Markovianity.

Abstract

We study the efficacy of the two recently introduced witnesses of non-Markovianity, namely that based on temporal correlations in pseudo-density matrix and temporal steering correlations in detecting information backflow. We show, through specific counterexamples taken from existing literature, that they can witness a process to be non-Markovian where trace distance and entropic distinguishability measures may fail. We further show that, since the pseudo-density matrix is directly related to the Choi matrix of a channel via the partial transpose, it can be generalized to quantify the total quantum memory in any indivisible process. Moreover, we make an interesting observation that temporal steerable correlations-based measure may not capture eternal non-Markovianity hence may not be proportional to Choi-matrix-based methods, while pseudo-density matrix-based measures introduced in this work faithfully capture eternal non-Markovianity. Our work highlights important distinction between weak and strong forms of quantum direct cause in quantum mechanics when applied to open system dynamics.