An efficient Quantum Private Query Protocol Based on Oracle and Grover Iteration

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Private query allows a client, Alice, to retrieve an item of a database hold by the server, Bob, without revealing which item he or she retrieved, while limiting his ability to access other items. In this paper, an efficient quantum private query (QPQ) protocol is proposed, where two oracle operations Ok, Od are utilized to encode the encryption keys and the encrypted data items into their corresponding quantum superposition states $\left | {\phi ^{\prime }} \right \rangle $ , $\left | {\psi ^{\prime }} \right \rangle $ , and the Grover iteration is also introduced to extract the target state $\left | {{d_{i}}^{\prime }} \right \rangle $ (i.e., the state of the encrypted data item Alice retrieved) from the superposition state. In order to guarantee the client’s privacy, the server Bob transmits all the encrypted data items of the database to the client Alice with oblivious transfer strategy. Compared with the previous qRAM-based or QKD-based QPQ protocols, our communication complexity (i.e., the number of transmitted qubits) is reduced from O(NlogN) or O(N) to O(logN), and the exchanged classical message is reduced from O(N) bits to O(logN) bits too. The security analysis shows our protocol can not only guarantee the server’s privacy but also the client’s privacy.