Noninvertibility and non-Markovianity of quantum dynamical maps

Abstract

We identify two broad types of noninvertibilities in quantum dynamical maps, one necessarily associated with CP indivisibility and one not so. We study the production of (non-)Markovian, invertible maps by the process of mixing noninvertible Pauli maps, and quantify the fraction of the same. The memory kernel perspective appears to be less transparent on the issue of invertibility than the approaches based on maps or master equations. Here we consider a related and potentially helpful issue: the identification of criteria of parameterized families of maps leading to the existence of a well-defined semigroup limit.

7 pages, 2 figures

References in corpus (7)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• An Invitation to Quantum Channels
• Markovian semigroup from mixing non-invertible 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
• Measure of invertible dynamical maps under convex combinations of noninvertible dynamical maps
• Non-Markovianity criteria for mixtures of noninvertible Pauli dynamical maps

Cited by in corpus (4)

• Extracting Dynamical Maps of Non-Markovian Open Quantum Systems
• Experimental realization of quantum non-Markovianity through the convex mixing of Pauli semigroups on an NMR quantum processor
• Violation of Diagonal Non-Invasiveness: A Hallmark of Non-Classical Memory Effects
• Efficient and operational quantifier of non-divisibility in terms of channel discrimination