Efficient semi-quantum private comparison without using entanglement resource and pre-shared key

Semi-quantum private comparison (SQPC) aims to compare the equality of the classical participants' secrets with the help of a semi-honest TP, in which TP has full quantum capability while the classical participants' quantum capability is limited. In the existing SQPC protocols, the entanglement resource (e.g., entangled state preparation and entangled state measurement) and pre-shared key are usually required. Besides, the qubit efficiency is relatively low. In this paper, we propose an efficient SQPC protocol based on single-particle states, in which the entanglement resource and pre-shared key are unnecessary. The qubit efficiency of our protocol is far greater than that of all existing SQPC protocols due to the use of single-particle states and circular transmission mode. Moreover, our protocol can be extended to the multi-party case, which can accomplish arbitrary pair's comparison of equality among n(n >= 2) classical participants. Finally, various kinds of attacks have been analyzed, which show that the proposed protocol is secure against the outside and inside attacks.