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Quantum private information retrieval (QPIR) for quantum messages is aquantum communication task, in which a user retrieves one of the multiplequantum states from the server without revealing which state is retrieved. Inthe one-server setting, we find an exponential gap in the communicationcomplexities between the presence and absence of prior entanglement in thisproblem with the one-server setting. To achieve this aim, as the first step, weprove that the trivial solution of downloading all messages is optimal underQPIR for quantum messages, which is a similar result to that of classical PIRbut different from QPIR for classical messages. As the second step, we proposean efficient one-server one-round QPIR protocol with prior entanglement byconstructing a reduction from a QPIR protocol for classical messages to a QPIRprotocol for quantum messages in the presence of prior entanglement.

Prior Entanglement Exponentially Improves One-Server Quantum Private Information Retrieval for Quantum Messages