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Comparative study of Bell's states

Balwant Singh Airy

Published Aug 1, 2019• 0 citations
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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.

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Recently, Liu et al. [ Commun. Theor. Phys. 57 (2012) 583 ] proposed a quantum private comparison protocol based on entanglement swapping of Bell states, which aims to securely compare the equality of two participants' information with the help of a semi-honest third party (TP). However, the present study points out there is a fatal loophole in Liu et al.'s protocol, and TP can make Bell-basis measurement to know all the participants' secret inputs without being detected. To fix the problem, a simple solution, which uses one-time eavesdropper checking with decoy photons instead of twice eavesdropper checking with Bell states, is demonstrated. Compared with the original protocol, it not only reduces the Bell states consumption but also simplifies the protocol steps.
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.