Observable bound for Gaussian illumination

TL;DR

This paper introduces observable bounds for Gaussian illumination to optimize signal-to-noise ratio in target detection, demonstrating quantum and classical regimes with different measurement strategies and performance limits.

Contribution

It derives observable bounds for Gaussian illumination and compares quantum and classical measurement strategies, highlighting their performance and implementation challenges.

Findings

Quantum regime receiver outperforms other feasible receivers.

Observable bounds are achieved with mode-by-mode measurements.

Classical regime receiver approaches the bound with photon number difference measurement.

Abstract

We propose observable bounds for Gaussian illumination to maximize the signal-to-noise ratio, which minimizes the discrimination error between the presence and absence of a low-reflectivity target using Gaussian states. The observable bounds are achieved with mode-by-mode measurements. In the quantum regime using a two-mode squeezed vacuum state, our observable receiver outperforms the other feasible receivers whereas it cannot approach the quantum Chernoff bound. The corresponding observable cannot be implemented with heterodyne detections due to the additional vacuum noise. In the classical regime using a thermal state, a receiver implemented with a photon number difference measurement approaches its bound regardless of the signal mean photon number, while it asymptotically approaches the classical bound in the limit of a huge idler mean photon number.