Detecting and quantifying non-Markovianity via quantum direct cause

Shrikant Utagi; Prateek Chawla

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arXiv · 2506.23267

Detecting and quantifying non-Markovianity via quantum direct cause

Shrikant Utagi·Prateek Chawla

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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.

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Shrikant Utagi, Prateek Chawla. 2025-06-29. Detecting and quantifying non-Markovianity via quantum direct cause. https://arxiv.org/abs/2506.23267

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