Error Probabilities of Quantum Illumination with Attenuation Using Maximum and Non-maximum Quasi-Bell States

Quantum illumination proposed by Lloyd is a protocol that detects the existence of a target by using entangled light of two-mode. Quantum illumination was first proposed using the Bell state, and then the use of a two-mode Gaussian state was proposed. On the other hand, there are many impact studies using the quasi-Bell state. However, as far as we know, there are no studies that analyze quantum illumination using the quasi-Bell state. Therefore, we focused on the performance evaluation of quantum illumination using the quasi-Bell state in this paper. We compared and considered the effects using the Bell state, the two-mode Gaussian state, the maximum quasi-Bell state, the non-maximum quasi-Bell state, and the coherent state (i.e., a laser radar) on the attenuated channel. In particular, we derived the exact solutions of the error probabilities when using the maximum and non-maximum quasi-Bell states. Then we clarified that quantum illumination using the quasi-Bell state offers a clear advantage over that using the other entangled states under almost situations and always offers a clear advantage over the laser radar.