Interference of Quantum Trajectories

TL;DR

This paper extends quantum trajectory theory to strongly coupled open quantum systems, introducing the influence martingale to model interference effects and enabling new numerical simulation methods.

Contribution

It proves that general time-local quantum master equations can be unraveled by jump-stochastic differential equations using the influence martingale, even at arbitrary coupling strengths.

Findings

Established a Markovian quantum trajectory framework for strongly coupled systems.

Introduced the influence martingale to account for interference effects.

Provided a new approach for numerically simulating large quantum systems.

Abstract

We extend quantum trajectory theory to encompass the evolution of a large class of open quantum systems interacting with an environment at {arbitrary coupling strength}. Specifically, we prove that general time-local quantum master equations admit an unraveling described by ordinary jump-stochastic differential equations. The sufficient condition is to weigh the state vector Monte Carlo averages by a probability pseudo-measure which we call the "influence martingale". The influence martingale satisfies a $ 1d $ stochastic differential equation enslaved to the ones governing the quantum trajectories. Our interpretation is that the influence martingale models interference effects between distinct realizations of quantum trajectories at strong system-environment coupling. Our result proves the existence of a Markovian quantum trajectory picture in the Hilbert space of the system for completely bounded divisible dynamical maps. Furthermore, our result provides a new avenue to numerically integrate systems with large numbers of degrees of freedom by naturally extending the existing theory.