Measure of invertible dynamical maps under convex combinations of noninvertible dynamical maps

Abstract

We study the convex combinations of the $(d+1)$-generalized Pauli dynamical maps in a Hilbert space of dimension $d$. For certain choices of the decoherence function, the maps are noninvertible, and they remain under convex combinations as well. For the case of dynamical maps characterized by the decoherence function $(1\ensuremath{-}{e}^{\ensuremath{-}ct})/n$ with the decoherence parameter $n$ and decay factor $c$, we evaluate the fraction of invertible maps obtained upon mixing, which is found to increase superexponentially with dimension $d$.