Microscopic biasing of discrete-time quantum trajectories

TL;DR

This paper introduces a microscopic method to bias quantum trajectories in discrete-time open quantum systems, making rare events typical by modifying the system's dynamics through additional collisions.

Contribution

It extends biased quantum trajectory theory from Lindblad dynamics to arbitrary sequences of dynamical maps with a clear physical interpretation.

Findings

Biasing achieved by modifying Kraus operators.

Extra collisions enforce desired rare trajectories.

Framework applies to general discrete quantum dynamics.

Abstract

We develop a microscopic theory for biasing the quantum trajectories of an open quantum system, which renders rare trajectories typical. To this end we consider a discrete-time quantum dynamics, where the open system collides sequentially with qubit probes which are then measured. A theoretical framework is built in terms of thermodynamic functionals in order to characterize its quantum trajectories (each embodied by a sequence of measurement outcomes). We show that the desired biasing is achieved by suitably modifying the Kraus operators describing the discrete open dynamics. From a microscopical viewpoint and for short collision times, this corresponds to adding extra collisions which enforce the system to follow a desired rare trajectory. The above extends the theory of biased quantum trajectories from Lindblad-like dynamics to sequences of arbitrary dynamical maps, providing at once a transparent physical interpretation.