The minimum error probability of quantum illumination

TL;DR

This paper proves that two-mode squeezed vacuum states are optimal for quantum illumination in asymmetric discrimination, providing a 6 dB advantage over classical states, and shows that more complex quantum states do not improve performance.

Contribution

It establishes the optimality of two-mode squeezed vacuum states for quantum illumination and introduces a new entropic inequality for noisy quantum Gaussian channels.

Findings

Two-mode squeezed vacuum states are optimal probes.

Quantum illumination with these states offers a 6 dB advantage.

No exotic quantum states outperform the optimal states in this scenario.

Abstract

Quantum illumination is a technique for detecting the presence of a target in a noisy environment by means of a quantum probe. We prove that the two-mode squeezed vacuum state is the optimal probe for quantum illumination in the scenario of asymmetric discrimination, where the goal is to minimize the decay rate of the probability of a false positive with a given probability of a false negative. Quantum illumination with two-mode squeezed vacuum states offers a 6 dB advantage in the error probability exponent compared to illumination with coherent states. Whether more advanced quantum illumination strategies may offer further improvements had been a longstanding open question. Our fundamental result proves that nothing can be gained by considering more exotic quantum states, such as e.g. multi-mode entangled states. Our proof is based on a new fundamental entropic inequality for the noisy quantum Gaussian attenuators. We also prove that without access to a quantum memory, the optimal probes for quantum illumination are the coherent states.