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arXiv:1805.11418 · Quantum Information Processing

Convex geometry of Markovian Lindblad dynamics and witnessing non-Markovianity

Bihalan Bhattacharya, Samyadeb Bhattacharya

Published Aug 1, 2021• 9 citations
arXivHTMLPDF
DOI
10.1007/s11128-021-03177-y

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Finite-time Markovian channels, unlike their infinitesimal counterparts, do not form a convex set. As a particular instance of this observation, we consider the problem of mixing the three Pauli channels, conservatively assumed to be quantum dynamical semigroups, and fully characterize the resulting ``Pauli simplex.'' We show that neither the set of non-Markovian (completely positive indivisible) nor Markovian channels is convex in the Pauli simplex, and that the measure of non-Markovian channels is about 0.87. All channels in the Pauli simplex are P divisible. A potential application in the context of quantum resource theory is also discussed.