Performance advantage of discriminating one-versus-two incoherent sources based on quantum hypothesis testing

TL;DR

This paper investigates the quantum limits of distinguishing one versus two incoherent sources in quantum imaging, proposing strategies that approach these limits in practical scenarios for improved detection.

Contribution

It introduces a quantum hypothesis testing framework for source discrimination, deriving error bounds and practical decision strategies without prior knowledge.

Findings

Error probabilities approach quantum lower bounds in one-shot and multi-shot tests.

Proposed strategies outperform prior-based guesses in source discrimination.

Analysis of challenges and solutions for realistic quantum imaging scenarios.

Abstract

Detecting the presence of multiple incoherent sources is a fundamental and challenging task for quantum imaging, especially within sub-Rayleigh region. In this paper, the discrimination of one-versus-two point-like incoherent sources in symmetric and asymmetric scenarios is studied. We calculate the quantum lower bounds on error probabilities of making a decision after one-shot and multi-shot tests. The results are compared with the error probability of prior-based direct guess, and the minimal number of tests required to make a decision outperforming direct guess is discussed. We also show the asymptotic quantum lower bound for a large number of tests. For practical purposes, we propose a specific strategy along with decision rule of which can work without any prior knowledge. With respect to each of two scenarios, the error probability can approach the quantum lower bound in one-shot test as well as multi-shot test. In addition, the potential challenges and solutions in a realistic scenario are analyzed. Our results may contribute to real-world quantum imaging such as microscopy and astronomy.