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

TL;DR

This paper investigates how convex combinations of generalized Pauli dynamical maps in high-dimensional quantum systems affect invertibility, revealing that the fraction of invertible maps increases rapidly with dimension.

Contribution

It provides a detailed analysis of the invertibility properties of convex combinations of noninvertible dynamical maps in high-dimensional spaces.

Findings

Fraction of invertible maps increases superexponentially with dimension

Convex combinations can restore invertibility in certain cases

Analysis focused on decoherence functions of the form (1-e^{-ct})/n

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 $d$.