Improved and formal proposal for device-independent quantum private query

In this paper, we present a novel quantum private query (QPQ) scheme that is fully device-independent. As far as we know, this is the first QPQ scheme that uses EPR pairs and offers full device independence. Our approach takes into account the self-testing of shared EPR pairs and the self-testing of projective measurement operators in a mistrustful scenario where neither the client nor the server trusts each other. To achieve full device independence, we also exploit self-testing of a specific class of POVM operators used by the client in our scheme. Additionally, we evaluate the performance of our proposal formally and derive an upper limit of the maximum cheating probabilities (when the protocol does not terminate) for both the dishonest client and the dishonest server. *This is a substantially revised and extended version of the paper [1] that recently appeared in the proceedings of Indocrypt 2022. This submitted version includes additional results in sections 1.1, 1.2, 1.4, 3.1, 3.3 and in the appendix.