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In the classical private information retrieval (PIR) setup, a user wants toretrieve a file from a database or a distributed storage system (DSS) withoutrevealing the file identity to the servers holding the data. In the quantum PIR(QPIR) setting, a user privately retrieves a classical file by receivingquantum information from the servers. The QPIR problem has been treated by Songet al. in the case of replicated servers, both with and without collusion. QPIRover $[n,k]$ maximum distance separable (MDS) coded servers was recentlyconsidered by Allaix et al., but the collusion was essentially restricted to$t=n-k$ servers in the sense that a smaller $t$ would not improve the retrievalrate. In this paper, the QPIR setting is extended to allow for retrieval withhigh rate for any number of colluding servers $t$ with $1 \leq t \leq n-k$.Similarly to the previous cases, the rates achieved are better than those knownor conjectured in the classical counterparts, as well as those of thepreviously proposed coded and colluding QPIR schemes. This is enabled byconsidering the stabilizer formalism and weakly self-dual generalizedReed--Solomon (GRS) star product codes.

High-Rate Quantum Private Information Retrieval with Weakly Self-Dual Star Product Codes