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 $d$.

arXiv comment6 pages, 1 figure

References in corpus (21)

• Quantum Computing in the NISQ era and beyond
• Quantum Resource Theories
• Entanglement and non-Markovianity of quantum evolutions
• Assessing non-Markovian dynamics
• Canonical form of master equations and characterization of non-Markovianity
• Non-Markovianity degree for random unitary evolution
• Eternal non-Markovianity: from random unitary to Markov chain realisations
• Pauli Diagonal Channels Constant on Axes
• Generalized Pauli channels and a class of non-Markovian quantum evolution
• Mixing-induced quantum non-Markovianity and information flow
• Markovian semigroup from non-Markovian evolutions
• An Invitation to Quantum Channels
• Convex Combinations of Pauli Semigroups: Geometry, Measure and an Application
• Singularity of dynamical maps
• Convex combinations of CP-divisible Pauli channels that are not semigroups
• 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
• Noninvertibility as a requirement for creating a semigroup under convex combinations of channels
• Measuring non-Markovianity via incoherent mixing with Markovian dynamics
• Non-Markovianity criteria for mixtures of noninvertible Pauli dynamical maps

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