Capacity of Quantum Private Information Retrieval with Colluding Servers

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 that the files except for the target file are not leaked to the user, and the t-private QPIR is 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. The full version is accessible at: https://arxiv.org/pdf/2001.04436.