Security improvements of several basic quantum private query protocols with O(log N) communication complexity

Abstract

New quantum private database (with N elements) query protocols are presented and analyzed. Protocols preserve O(log⁡N) communication complexity of known protocols for the same task, but achieve several significant improvements in security, especially concerning user privacy. For example, the randomized form of our protocol has a cheat-sensitive property – it allows the user to detect a dishonest database with a nonzero probability, while the phase-encoded private query protocols [6,7] for the same task do not have such a property. Moreover, when the database performs the computational basis measurement, a particular projective measurement which can cause a significant loss of user privacy in the previous private query protocols with O(log⁡N) communication complexity, at most half of the user privacy could leak to such a database in our protocol, while in the QPQ protocol [5], the entire user privacy could leak out. In addition, it is proved here that for large N, the user could detect a cheating via the computational basis measurement, with a probability close to 12 using O(N) special queries. Finally, it is shown here, for both forms of our protocol, basic and randomized, how a dishonest database has to act in case it could not learn user's queries.