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.