Markovian semigroup from mixing non-invertible dynamical maps

Abstract

We analyze the convex combinations of non-invertible generalized Pauli dynamical maps. By manipulating the mixing parameters, one can produce a channel with shifted singularities, additional singularities, or even no singularities whatsoever. In particular, we show how to use non-invertible dynamical maps to produce the Markovian semigroup. Interestingly, the maps whose mixing results in a semigroup are generated by the time-local generators and time-homogeneous memory kernels that are not regular; i.e., their formulas contain infinities. Finally, we show how the generators and memory kernels change after mixing the corresponding dynamical maps.

References in corpus (19)

• Non-Markovian dynamics in open quantum systems
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• 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
• Finding the Kraus decomposition from a master equation and vice versa
• Simulation of indivisible qubit channels in collision models
• Eternal non-Markovianity: from random unitary to Markov chain realisations
• Sufficient conditions for memory kernel master equation
• 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
• On generalized semi-Markov quantum evolution
• On admissible memory kernels for random unitary qubit evolution
• Markovian semigroup from non-Markovian evolutions
• Convex Combinations of Pauli Semigroups: Geometry, Measure and an Application
• Quantum channels irreducibly covariant with respect to the finite group generated by the Weyl operators
• Memory kernel approach to generalized Pauli channels: Markovian, semi-Markov, and beyond
• Convex combinations of CP-divisible Pauli channels that are not semigroups

Cited by in corpus (11)

• Space-time dual quantum Zeno effect: Interferometric engineering of open quantum system dynamics
• Approximating Invertible Maps by Recovery Channels: Optimality and an Application to Non-Markovian Dynamics
• 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
• Quantifying non-Markovianity via local quantum Fisher information
• 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
• Accessible maps in a group of classical or quantum channels