Solvable class of non-Markovian quantum multipartite dynamics

We study a class of multipartite open quantum dynamics for systems with an 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 the 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.

Figure 1

Scaled time-dependent rates [Eqs. (25) and (26)] corresponding to the multipartite trigonometric eternal non-Markovian evolution [Eq. (23)] for different values of the rate ratio $\phi /\gamma .$

Figure 2

(Dimensionless) CPF correlation [Eq. (36)] corresponding to the eternal non-Markovian trigonometric model [Eq. (23)] for different values of $\phi /\gamma$ and measurement time-interval relations $\tau /t.$ In all cases, the system initial condition is such that $\langle x\rangle =0.$