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arXiv · 1910.04114

Convex Combinations of Pauli Semigroups: Geometry, Measure and an Application

Vinayak Jagadish·R. Srikanth·Francesco Petruccione
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Abstract

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.

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Vinayak Jagadish, R. Srikanth, Francesco Petruccione. 2019-10-09. Convex Combinations of Pauli Semigroups: Geometry, Measure and an Application. https://doi.org/10.1103/physreva.101.062304

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