Noninvertibility as a requirement for creating a semigroup under convex combinations of channels

Abstract

We study the conditions under which a semigroup is obtained upon convex combinations of channels. In particular, we study the set of Pauli and generalized Pauli channels. We find that mixing only semigroups can never produce a semigroup. Counter-intuitively, we find that for a convex combination to yield a semigroup, most of the input channels have to be noninvertible.

5 pages

References in corpus (5)

• Pauli Diagonal Channels Constant on Axes
• An Invitation to Quantum Channels
• Markovian semigroup from mixing non-invertible dynamical maps
• Singularities, mixing and non-Markovianity of Pauli dynamical maps
• Measure of not-completely-positive qubit maps: the general case

Cited by in corpus (4)

• Measure of invertible dynamical maps under convex combinations of noninvertible 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