Signal-to-noise ratio of Gaussian-state ghost imaging

TL;DR

This paper derives and compares the signal-to-noise ratios of three Gaussian-state ghost imaging setups, revealing how classical and quantum light sources influence imaging performance in different regimes.

Contribution

It provides analytic SNR expressions for classical and nonclassical Gaussian-state ghost imaging, including asymptotic approximations for various brightness levels and regimes.

Findings

High-brightness thermal sources often outperform biphoton sources in SNR.

Entangled sources can surpass thermal sources with high-efficiency detectors at low brightness.

Analytic formulas enable optimized ghost imaging system design.

Abstract

The signal-to-noise ratios (SNRs) of three Gaussian-state ghost imaging configurations--distinguished by the nature of their light sources--are derived. Two use classical-state light, specifically a joint signal-reference field state that has either the maximum phase-insensitive or the maximum phase-sensitive cross correlation consistent with having a proper $P$ representation. The third uses nonclassical light, in particular an entangled signal-reference field state with the maximum phase-sensitive cross correlation permitted by quantum mechanics. Analytic SNR expressions are developed for the near-field and far-field regimes, within which simple asymptotic approximations are presented for low-brightness and high-brightness sources. A high-brightness thermal-state (classical phase-insensitive state) source will typically achieve a higher SNR than a biphoton-state (low-brightness, low-flux limit of the entangled-state) source, when all other system parameters are equal for the two systems. With high efficiency photon-number resolving detectors, a low-brightness, high-flux entangled-state source may achieve a higher SNR than that obtained with a high-brightness thermal-state source.