Quantum Private Information Retrieval for Quantum Messages

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.

References in corpus (7)

• Insecurity of Quantum Secure Computations
• Private Information Retrieval from Coded Databases with Colluding Servers
• Universal Quantum Information Compression
• Limits for compression of quantum information carried by ensembles of mixed states
• Exponents of quantum fixed-length pure state source coding
• Quantum Private Information Retrieval has linear communication complexity
• Towards the Capacity of Private Information Retrieval from Coded and Colluding Servers