Confidence and Backaction in the Quantum Filter Equation

TL;DR

This paper investigates how confidence and backaction influence quantum state estimation using continuous weak measurements, with a focus on double quantum dots and the role of quantum discord in confidence bounds.

Contribution

It introduces a framework for quantifying confidence and backaction in quantum filtering, linking confidence bounds to quantum discord for general measurements.

Findings

Confidence in state estimates can be quantified using relative entropy.

Backaction affects the accuracy of quantum state reconstruction.

Quantum discord provides a lower bound on confidence in measurements.

Abstract

We study the confidence and backaction of state reconstruction based on a continuous weak measurement and the quantum filter equation. As a physical example we use the traditional model of a double quantum dot being continuously monitored by a quantum point contact. We examine the confidence of the estimate of a state constructed from the measurement record, and the effect of backaction of that measurement on that state. Finally, in the case of general measurements we show that using the relative entropy as a measure of confidence allows us to define the lower bound on the confidence as a type of quantum discord.