Smoothed quantum-classical states in time-irreversible hybrid dynamics

TL;DR

This paper introduces a method to infer a smoothed joint quantum-classical state in time-irreversible hybrid dynamics, improving state purity estimates without needing unobserved measurement data.

Contribution

It develops a smoothing technique for hybrid quantum-classical states, extending previous filtering methods to incorporate both past and future measurement information.

Findings

Smoothed states provide higher purity than filtering states.

The method accurately recovers joint dynamics in dissipative systems.

Application to fluorescent systems demonstrates practical benefits.

Abstract

We consider a quantum system continuously monitored in time which in turn is coupled to an arbitrary dissipative classical system (diagonal reduced density matrix). The quantum and classical dynamics can modify each other, being described by an arbitrary time-irreversible hybrid Lindblad equation. Given a measurement trajectory, a conditional bipartite stochastic state can be inferred by taking into account all previous recording information (filtering). Here, we demonstrate that the joint quantum-classical state can also be inferred by taking into account both past and future measurement results (smoothing). The smoothed hybrid state is estimated without involving information from unobserved measurement channels. Its average over recording realizations recovers the joint time-irreversible behavior. As an application we consider a fluorescent system monitored by an inefficient photon detector. This feature is taken into account through a fictitious classical two-level system. The average purity of the smoothed quantum state increases over that of the (mixed) state obtained from the standard quantum jump approach.