Quantum Illumination Advantage for Classification Among an Arbitrary Library of Targets

TL;DR

This paper demonstrates that quantum illumination provides a fourfold improvement over classical methods in discriminating among multiple targets in high-loss, high-noise environments, extending previous results to arbitrary target libraries.

Contribution

It proves that quantum illumination offers a significant advantage in target discrimination among multiple known targets, generalizing prior results beyond simple detection.

Findings

Quantum illumination achieves a fourfold increase in error discrimination exponent.

The advantage holds for arbitrary target libraries, not just presence/absence detection.

Derived analytic expressions for quantum and classical Chernoff exponents.

Abstract

Quantum illumination (QI) is the task of querying a scene using a transmitter probe whose quantum state is entangled with a reference beam retained in ideal storage, followed by optimally detecting the target-returned light together with the stored reference, to make decisions on characteristics of targets at stand-off range, at precision that exceeds what is achievable with a classical transmitter of the same brightness and otherwise identical conditions. Using tools from perturbation theory, we show that in the limit of low transmitter brightness, high loss, and high thermal background, there is a factor of four improvement in the Chernoff exponent of the error probability in discriminating any number of apriori-known reflective targets when using a Gaussian-state entangled QI probe, over using classical coherent-state illumination (CI). While this advantage was known for detecting the presence or absence of a target, it had not been proven for the generalized task of discriminating between arbitrary target libraries. In proving our result, we derive simple general analytic expressions for the lowest-order asymptotic expansions of the quantum Chernoff exponents for QI and CI in terms of the signal brightness, loss, thermal noise, and the modal expansion coefficients of the target-reflected light's radiant exitance profiles when separated by a spatial mode sorter after entering the entrance pupil of the receiver's aperture.