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arXiv:2109.02335 · International Journal of Quantum Information

Non-Markovianity and entanglement detection

Sourav Chanduka, Bihalan Bhattacharya, Rounak Mundra, Samyadeb Bhattacharya, Indranil Chakrabarty

Published May 20, 2023• 1 citation
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Abstract

We have established a novel method to detect non-Markovian indivisible quantum channels using structural physical approximation. We have shown that this method can be used to detect eternal non-Markovian operations. We have further established that harnessing eternal non-Markovianity, we can device a protocol to detect quantum entanglement.

DOI
10.1142/s0219749923500259

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We devise a novel protocol to detect genuinely multipartite entangled states by harnessing quantum non-Markovian operations. We utilize a particular type of non-Markovianity known as the eternal non-Markovianity to construct a non-complete positive map to filter out the bi-separable states and detect genuine multipartite entanglement. We further propose a dynamical procedure to detect genuinely multipartite entangled states in real-time based on this theory. Our study sheds light on a hitherto unexplored connection between entanglement theory and quantum non-Markovianity.
Abstract We devise a novel protocol to detect genuinely multipartite entangled states by harnessing quantum non-Markovian operations. We utilize a particular type of non-Markovianity known as the eternal non-Markovianity to construct a non-complete positive map to filter out the bi-separable states and detect genuine multipartite entanglement. We further propose a witness operator to detect genuinely multipartite entangled states experimentally based on this theory. Our study sheds light on a hitherto unexplored connection between entanglement theory and quantum non-Markovianity.
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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.