Hypothesis testing with a continuously monitored quantum system

TL;DR

This paper investigates how continuous quantum measurements and optimal final state measurements can improve hypothesis testing accuracy in quantum systems, specifically analyzing a driven two-level system's radiative decay.

Contribution

It introduces a framework combining continuous monitoring and optimal final measurements for quantum hypothesis testing, with detailed analysis of a two-level system's decay.

Findings

Photon counting and homodyne detection enhance information extraction.

Optimal projective measurement improves hypothesis discrimination.

Results approach theoretical lower bounds for error probability.

Abstract

In a Bayesian analysis, the likelihood that specific candidate parameters govern the evolution of a quantum system are conditioned on the outcome of measurements which, in turn, cause measurement backaction on the state of the system [M. Tsang, Phys. Rev. Lett. 108, 170502 (2012)]. Specializing to the distinction of two candidate hypotheses, we study the achievements of continuous monitoring of the radiation emitted by a quantum system followed by an optimal projective measurement on its conditioned final state. Our study of the radiative decay of a driven two-level system shows an intricate interplay between the maximum information available from photon counting and homodyne detection and the final projective measurement on the emitter. We compare the results with theory predicting a lower bound for the probability to assign a wrong hypothesis by any combined measurement on the system and its radiative environment.