A solvable class of non-Markovian quantum multipartite dynamics

TL;DR

This paper introduces a class of exactly solvable non-Markovian quantum dynamics for multipartite qubit systems, characterizing conditions for complete positivity and exploring memory effects with novel hyperbolic and trigonometric models.

Contribution

It formulates general constraints for complete positivity in non-Markovian multipartite quantum dynamics and derives new solvable models with explicit time-dependent rates.

Findings

Identified conditions for complete positivity in complex non-Markovian systems.

Derived hyperbolic and trigonometric non-Markovian master equations.

Explored memory effects using operational witnesses.

Abstract

We study a class of multipartite open quantum dynamics for systems of arbitrary number of qubits. The non-Markovian quantum master equation can involve arbitrary single or multipartite and time-dependent dissipative coupling mechanisms, expressed in terms of strings of Pauli operators. We formulate the general constraints that guarantee the complete positivity of this dynamics. We characterize in detail underlying mechanisms that lead to memory effects, together with properties of the dynamics encoded in the associated system rates. We specifically derive multipartite "eternal" non-Markovian master equations that we term hyperbolic and trigonometric due to the time dependence of their rates. For these models we identify a transition between positive and periodically divergent rates. We also study non-Markovian effects through an operational (measurement-based) memory witness approach.