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

• URL: http://arxiv.org/abs/2201.03258v3
• Date: Thu, 28 Jul 2022 17:44:52 GMT
• Title: Measure of invertible dynamical maps under convex combinations of noninvertible dynamical maps
• Authors: Vinayak Jagadish, R. Srikanth, Francesco Petruccione
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $d$.

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