Quantum detection for on-off keyed mixed-state signals with a small amount of thermal noise

The detection strategy proposed previously by the authors for binary pure-state signals, which consists of a unitary transformation and photon counting afterward [Phys. Rev. A 54, 2728 (1996)], can also be applied to the case of on-off keyed signals of coherent states with a small amount of thermal noise. It yields an error level almost the same as the quantum minimum bound in practical parameter region.