Adaptive identification of coherent states

TL;DR

This paper introduces an adaptive measurement method for efficiently characterizing optical coherent states by dynamically adjusting measurement settings based on collected data, significantly reducing the number of measurements needed.

Contribution

The authors develop a two-step adaptive algorithm that improves measurement efficiency for coherent states, incorporating stochastic decision-making and error robustness enhancements.

Findings

Reduces measurement shots by a factor proportional to initial uncertainty area.

Effectively distinguishes vacuum and photon detection to refine state estimation.

Enhances robustness with repeated measurements in the initial step.

Abstract

We present methods for efficient characterization of an optical coherent state $|\alpha\rangle$. We choose measurement settings adaptively and stochastically, based on data while it is collected. Our algorithm divides the estimation into two distinct steps: (i) before the first detection of a vacuum state, the probability of choosing a measurement setting is proportional to detecting vacuum with the setting, which makes using too similar measurement settings twice unlikely; and (ii) after the first detection of vacuum, we focus measurements in the region where vacuum is most likely to be detected. In step (i) [(ii)] the detection of vacuum (a photon) has a significantly larger effect on the shape of the posterior probability distribution of $\alpha$. Compared to nonadaptive schemes, our method makes the number of measurement shots required to achieve a certain level of accuracy smaller approximately by a factor proportional to the area describing the initial uncertainty of $\alpha$ in phase space. While this algorithm is not directly robust against readout errors, we make it such by introducing repeated measurements in step (i).