Capacity of Quantum Private Information Retrieval with Colluding Servers
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Quantum private information retrieval (QPIR) is a protocol that a user retrieves a file from non-communicating servers by downloading quantum systems without revealing the identity of the target file. We study the -private QPIR that the identity of the target file is kept secret even if at most servers may collude to reveal the identity. As a result, we prove that the -private QPIR capacity is 1 for 1≤≤/2 and 2(-)/ for /2 < <, where the QPIR capacity is the maximum rate of the file size over the size of downloaded quantum systems. We construct a capacity-achieving QPIR protocol with zero-error and perfect user secrecy against the collusion of servers. Our protocol also achieves the server secrecy, i.e., the user obtains no other information than the target file. We also prove the optimality of our protocol with converse bounds.
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