Secure Quantum Private Comparison of Equality Based on Asymmetric W State

Recently, Liu et al. (Opt. Commun. 284:3160, 2011) proposed a protocol for quantum private comparison of equality (QPCE) based on symmetric W state. However, Li et al. (Eur. Phys. J. D 66:110, 2012) pointed out that there is a flaw of information leak, and they proposed a new protocol based on EPR pairs. While examining these two protocols, we find that there exists a same flaw: the third party (TP) can know the comparison result. In this paper, through introducing and constructing a special class of asymmetric W state, a secure QPCE protocol based on this asymmetric W state is presented. Analysis shows the present protocol can not only effectively avoid the information leak found by Li et al., but also ensure TP would not get any information about the comparison result.