Convex combinations of CP-divisible Pauli channels that are not semigroups

Abstract

We study the memory property of the channels obtained by convex combinations of Markovian channels that are not necessarily quantum dynamical semigroups (QDSs). In particular, we characterize the geometry of the region of (non-)Markovian channels obtained by the convex combination of the three Pauli channels, as a function of deviation from the semigroup form in a family of channels. The regions are highly convex, and interestingly, the measure of the non-Markovian region shrinks with greater deviation from the QDS structure for the considered family, underscoring the counterintuitive nature of (non-)Markovianity under channel mixing.

arXiv comment5 pages, 4 figures

References in corpus (22)

• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Non-Markovian dynamics in open quantum systems
• Entanglement and non-Markovianity of quantum evolutions
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Assessing non-Markovian dynamics
• Canonical form of master equations and characterization of non-Markovianity
• Concepts of quantum non-Markovianity: a hierarchy
• Non-Markovian quantum dynamics: local versus non-local
• Markovian and non-Markovian dynamics in quantum and classical systems
• Quantum Semi-Markov Processes
• Non-Markovianity degree for random unitary evolution
• Eternal non-Markovianity: from random unitary to Markov chain realisations
• Non-Markovian quantum dynamics: What is it good for?
• Non-Markovian quantum dynamics: What does it mean?
• Temporal self-similarity of quantum dynamical maps as a concept of memorylessness
• Mixing-induced quantum non-Markovianity and information flow
• On generalized semi-Markov quantum evolution
• Non-Markovianity through quantum coherence in an all-optical setup
• Markovian semigroup from non-Markovian evolutions
• An Invitation to Quantum Channels
• Convex Combinations of Pauli Semigroups: Geometry, Measure and an Application
• Pauli semigroups and unistochastic quantum channels

Cited by in corpus (14)

• Interferometric Approach to Open Quantum Systems and Non-Markovian Dynamics
• Markovian semigroup from mixing non-invertible dynamical maps
• Singularities, mixing and non-Markovianity of Pauli dynamical maps
• Invertibility as a witness of Markovianity of the quantum dynamical maps
• Noninvertibility as a requirement for creating a semigroup under convex combinations of channels
• Measure of invertible dynamical maps under convex combinations of noninvertible dynamical maps
• A solvable class of non-Markovian quantum multipartite dynamics
• Non-Markovianity criteria for mixtures of noninvertible Pauli dynamical maps
• Noninvertibility and non-Markovianity of quantum dynamical maps
• Log-Convex set of Lindblad semigroups acting on $N$-level system
• Phase-covariant mixtures of non-unital qubit maps
• Experimental realization of quantum non-Markovianity through the convex mixing of Pauli semigroups on an NMR quantum processor
• Geometry of symmetric and non-invertible Pauli channels
• Digital simulation of convex mixtures of Markovian and non-Markovian single qubit Pauli channels on NISQ devices