Capacity of Quantum Private Information Retrieval with Collusion of All But One of Servers
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Quantum private information retrieval (QPIR) is the problem to retrieve one of f classical files by downloading quantum systems from non-communicating n servers each of which contains the copy of f files, while the identity of the retrieving file is unknown to each server. As an extension, we consider the colluded QPIR that the identity of the retrieving file is secret even if any n-1 servers collude, and derive the QPIR capacity for this problem which is defined as the maximum rate of the retrieving file size over the download size. For an even number n of servers, we show that the capacity of the colluded QPIR is 2/n, when we assume that there are preexisting entanglements among the servers and require that no information of the non-retrieving files is retrieved. We construct a colluded QPIR protocol of rate n/2^-1 and prove that the capacity is upper bounded by 2/n. The colluded QPIR capacity is strictly higher than the classical counterpart.
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