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 $(1-e^{-ct})/n$ 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 $d$.

6 pages, 1 figure

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Cited by in corpus (4)

• Noninvertibility and non-Markovianity of quantum dynamical maps
• Enhancing phase-covariant channel performance with non-unitality
• Experimental realization of quantum non-Markovianity through the convex mixing of Pauli semigroups on an NMR quantum processor
• Spin-1 teleportation-based quantum state tomography