A comparison between quantum and classical noise radar sources

TL;DR

This paper compares quantum and classical noise radar sources, demonstrating quantum advantage in cross-mode correlations and error decay rates under certain conditions, but showing no advantage with amplification or separate measurements.

Contribution

It provides a detailed comparison of quantum and classical radar performance, highlighting conditions where quantum correlations offer benefits and limitations.

Findings

Quantum radar shows a $\sqrt{2}$ advantage in cross-mode correlations.

No quantum advantage is observed with high gain amplification.

Quantum setup's error decay rate exceeds classical by $\ln(1+1/N_S)$ in low photon number regime.

Abstract

We compare the performance of a quantum radar based on two-mode squeezed states with a classical radar system based on correlated thermal noise. With a constraint of equal number of photons $N_S$ transmitted to probe the environment, we find that the quantum setup exhibits an advantage with respect to its classical counterpart of $\sqrt{2}$ in the cross-mode correlations. Amplification of the signal and the idler is considered at different stages of the protocol, showing that no quantum advantage is achievable when a large-enough gain is applied, even when quantum-limited amplifiers are available. We also characterize the minimal type-II error probability decay, given a constraint on the type-I error probability, and find that the optimal decay rate of the type-II error probability in the quantum setup is $\ln(1+1/N_S)$ larger than the optimal classical setup, in the $N_S\ll1$ regime. In addition, we consider the Receiver Operating Characteristic (ROC) curves for the scenario when the idler and the received signal are measured separately, showing that no quantum advantage is present in this case. Our work characterizes the trade-off between quantum correlations and noise in quantum radar systems.