Classical benchmarking for microwave quantum illumination

Quantum illumination theoretically promises up to a 6 dB error-exponent advantage in target detection over the best classical protocol. The advantage is maximised by a regime that includes a very high background, which occurs naturally when one considers microwave operation. Such a regime has well-known practical limitations, though it is clear that, theoretically, knowledge of the associated classical benchmark in the microwave is lacking. The requirement of amplifiers for signal detection necessarily renders the optimal classical protocol here different to that which is traditionally used, and only applicable in the optical domain. This work outlines what is the true classical benchmark for the microwave Quantum illumination using coherent states, providing new bounds on error probability and closed formulae for the receiver operating characteristic, for both optimal (based on quantum relative entropy) and homodyne detection schemes. An alternative source generation procedure based on coherent states is also proposed, which demonstrates the potential to make classically optimal performances achievable in optical applications. The same bounds and measures for the performance of such a source are provided, and its potential utility in the future of room temperature quantum detection schemes in the microwave is discussed.