Reducing the communication complexity of quantum private database queries by subtle classical post-processing with relaxed quantum ability

Abstract

Existing protocols for private database queries in the quantum context are classified into two-dimensional protocols and d-dimensional ones. For the two-dimensional protocols, to obtain a meaningful n-bit message from the database, the user Alice has to query n times to get all the n bits. However, each query may leak Alice's privacy once the server Bob obtains the address she queried, since each queried bit contributes to the whole queried message. Apparently, the longer the queried message is, the worse the user privacy becomes. By contrast, the d-dimensional protocol allows the user to query a multi-bit block with length no more than logd from the database via only one query. In this paper, we propose a novel d-dimensional quantum protocol for private database query. In contrast to existing d-dimensional protocols, the proposed protocol allows the user to retrieve a message of theoretically arbitrary length without the limitation of the dimension d by using a subtle classical post-processing strategy. Furthermore, the server's outcomes of measurement can be irrelevant for the implementation of the protocol thus relaxing his/her quantum ability. Finally, the security of the proposed protocol in the zero-error case has been proved in terms of the user privacy and database security.