We propose a protocol of quantum privacy comparison with polarization-entangled Einstein-Podolsky-Rosen (Bell) states and the coherent states. One of two legitimate participants, Alice, prepares polarization-entangled Bell states and keeps one photon of each photon pair and sends the other photons to the third party, Charlie. Receiving the photons, Charlie performs single-photon transformation operations on them and then sends them to the other legitimate participant, Bob. Three participants adopt parity analysis method to check the distribution security of Bell states. Exploiting polarization beam splitters and nonlinear interactions mediated by the probe coherent states in Kerr media, Alice and Bob check the parities of their photons using the bases of $\{\ket H, \ket V\}$ or $\{\ket +, \ket -\}$. On the basis of the parity analysis outcomes and Charlie's publicized information, they can analyze the security of the distributed quantum channel. Confirming secure distribution of the shared Bell states, two participants perform respective parity measurements on the privacy photons and own photons of Bell states, and then send the results to Charlie. According to information provided by two legitimate participants and his single-qubit transformation operations, Charlie compares the privacy information of Alice and Bob and publicizes the conclusion.
Non-Gaussianity of quantum states: An experimental test on single-photon-added coherent states
