# The ultimate precision of quantum illumination. (arXiv:1802.02158v1 [quant-ph])

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 minimizing 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.