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

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.

arXiv comment5 pages, 1 figure

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Cited by in corpus (16)

• Convex combinations of CP-divisible Pauli channels that are not semigroups
• Markovian semigroup from mixing non-invertible dynamical maps
• Space-time dual quantum Zeno effect: Interferometric engineering of open quantum system dynamics
• Local disclosure of quantum memory in non-Markovian dynamics
• Singularities, mixing and non-Markovianity of Pauli dynamical maps
• Invertibility as a witness of Markovianity of the quantum dynamical maps
• Measure of invertible dynamical maps under convex combinations of noninvertible dynamical maps
• Noninvertibility as a requirement for creating a semigroup under convex combinations of channels
• A solvable class of non-Markovian quantum multipartite dynamics
• Non-Markovianity criteria for mixtures of noninvertible Pauli dynamical maps
• Noninvertibility and non-Markovianity of quantum dynamical maps
• Phase-covariant mixtures of non-unital qubit maps
• Experimental realization of quantum non-Markovianity through the convex mixing of Pauli semigroups on an NMR quantum processor
• Geometry of symmetric and non-invertible Pauli channels
• Normal quantum channels and Markovian correlated two-qubit quantum errors
• Accessible maps in a group of classical or quantum channels