Quantum State Smoothing

TL;DR

This paper introduces a quantum state smoothing technique that conditions a quantum state on all-time measurement records, enhancing state estimation accuracy for open quantum systems.

Contribution

It defines a smoothed quantum state conditioned on all-time measurements and analyzes how different unravellings influence state purity improvements.

Findings

Smoothed quantum states can be more pure than filtered states.

Choice of unravelling affects the purity increase.

Method provides a new way to estimate quantum states more accurately.

Abstract

Smoothing is an estimation method whereby a classical state (probability distribution for classical variables) at a given time is conditioned on all-time (both past and future) observations. Here we define a smoothed quantum state for a partially monitored open quantum system, conditioned on an all-time monitoring-derived record. We calculate the smoothed distribution for a hypothetical unobserved record which, when added to the real record, would complete the monitoring, yielding a pure-state "quantum trajectory". Averaging the pure state over this smoothed distribution yields the (mixed) smoothed quantum state. We study how the choice of actual unravelling affects the purity increase over that of the conventional (filtered) state conditioned only on the past record.