Detecting changes to sub-diffraction objects with quantum-optimal speed and accuracy

TL;DR

This paper establishes the fundamental limits of change detection in sub-diffraction imaging and demonstrates that quantum-optimal measurements significantly outperform conventional intensity detection, approaching the theoretical best latency.

Contribution

It analytically derives the quantum limit for change detection latency in sub-diffraction imaging and shows that spatial-mode demultiplexing achieves this limit, outperforming traditional intensity detection.

Findings

Quantum-optimal measurement achieves the lowest possible detection latency.

Spatial-mode demultiplexing approaches the quantum limit.

Conventional intensity detection is sub-optimal for change detection in sub-diffraction objects.

Abstract

Detecting if and when objects change is difficult in passive sub-diffraction imaging of dynamic scenes. We consider the best possible tradeoff between responsivity and accuracy for detecting a change from one arbitrary object model to another in the context of sub-diffraction incoherent imaging. We analytically evaluate the best possible average latency, for a fixed false alarm rate, optimizing over all physically allowed measurements of the optical field collected by a finite 2D aperture. We find that direct focal-plane detection of the incident optical intensity achieves sub-optimal detection latencies compared to the best possible average latency, but that a three-mode spatial-mode demultiplexing measurement in concert with on-line statistical processing using the well-known CUSUM algorithm achieves this quantum limit for sub-diffraction objects. We verify these results via Monte Carlo simulation of the change detection procedure and quantify a growing gap between the conventional and quantum-optimal receivers as the objects are more and more diffraction-limited.