Solvable class of non-Markovian quantum multipartite dynamics

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 timedependent 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.

Quantum non-Markovian environment-to-system backflows of information: non-operational vs. operational approaches

“…Explicit general expression for C pf (t, τ )| y in terms of the coefficients {g j k (t)} can be found in Ref. [39] (see corresponding Appendix D). Under the previous assumptions, the CPF correlation can be obtained in an analytical way, which is written in [40].…”