Stochastic unraveling of positive quantum dynamics

Abstract

Stochastic unravelings represent a useful tool to describe the dynamics of open quantum systems, and standard methods, such as quantum state diffusion (QSD), call for the complete positivity of the open-system dynamics. Here, we present a generalization of QSD, which also applies to positive, but not completely positive evolutions. The rate and the action of the diffusive processes involved in the unraveling are obtained by applying a proper transformation to the operators which define the master equation. The unraveling is first defined for semigroup dynamics and then extended to a definite class of time-dependent generators. We test our approach on a prototypical model for the description of exciton transfer, keeping track of relevant phenomena, which are instead disregarded within the standard, completely positive framework.

Quantum trajectories for time-dependent adiabatic master equations

“…While a vast literature exists on the topic of quantum trajectories for time-independent master equations, much less is known for the case of time-dependent master equations (see, e.g., Ref. [10]), which is our focus here. Specifically, we focus on the case of open systems evolving adiabatically according to a time-dependent Hamiltonian, weakly coupled to the environment [11,12].…”

“…The condition on γ i (ω, t) such that the map is P-divisible can be found in the proof given in[18] or Eq. (25) in[10].…”

New results on non-CP dynamics unearthed from urtexts of quantum state diffusion

“…As pointed out correctly in [10], these conditions are equivalent with the positivity (9) of the transition rate operator. Quantum State Diffusion.…”

“…This theorem was explicitly stated and re-derived in [10], starting from the oldest conditions of Kossakowski [11] which [2] quoted in the following invariant form. The…”

“…Jump unraveling of a non-CP master equation in 2D appeared next in [9] only. Very recently a detailed work [10] has extended QSD for non-CP master equations.…”