Quantum Private Information Retrieval for Quantum Messages

TL;DR

This paper explores quantum private information retrieval protocols for quantum messages, establishing optimality results for single-server cases and proposing efficient multi-server protocols with privacy guarantees under various settings.

Contribution

It proves the optimality of trivial solutions in certain single-server scenarios and introduces new multi-server symmetric QPIR protocols with enhanced privacy features.

Findings

Trivial solutions are optimal for one-server blind QPIR.

Shared entanglement enables efficient one-server blind QPIR protocols.

Constructed three two-server symmetric QPIR protocols for pure states.

Abstract

Quantum private information retrieval (QPIR) for quantum messages is the protocol in which a user retrieves one of the multiple quantum states from one or multiple servers without revealing which state is retrieved. We consider QPIR in two different settings: the blind setting, in which the servers contain one copy of the message states, and the visible setting, in which the servers contain the description of the message states. One trivial solution in both settings is downloading all states from the servers and the main goal of this paper is to find more efficient QPIR protocols. First, we prove that the trivial solution is optimal for one-server QPIR in the blind setting. In one-round protocols, the same optimality holds even in the visible setting. On the other hand, when the user and the server share entanglement, we prove that there exists an efficient one-server QPIR protocol in the blind setting. Furthermore, in the visible setting, we prove that it is possible to construct symmetric QPIR protocols in which the user obtains no information of the non-targeted messages. We construct three two-server symmetric QPIR protocols for pure states. Note that symmetric classical PIR is impossible without shared randomness unknown to the user.