Seunghoan Song

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 two-server symmetric QPIR protocols. Note that symmetric classical PIR is impossible without shared randomness unknown to the user.

Quantum private information retrieval (QPIR) is a protocol that a user retrieves one of f files from non- communicating n servers by downloading quantum systems without revealing the identity of the target file. As variants of the QPIR with stronger security requirements, the symmetric QPIR is a protocol that the files except for the target file are not leaked to the user, and the t-private QPIR is a protocol that the identity of the target file is kept secret even if at most t servers may collude to reveal the identity. The QPIR capacity is the maximum ratio of the one file size to the size of downloaded quantum systems, and we prove that the symmetric t-private QPIR capacity is min{1, 2(n − t)/n} for any 1 ≤ t < n. We construct a capacity-achieving QPIR protocol by the stabilizer formalism and prove the optimality of our protocol. The proposed capacity is greater than the classical counterpart.