Quantum Private Information Retrieval from MDS-coded and Colluding Servers

In the classical private information retrieval (PIR) setup, a user wants to retrieve a file from a database or a distributed storage system (DSS) without revealing the file identity to the servers holding the data. In the quantum PIR (QPIR) setting, a user privately retrieves a classical file by downloading quantum systems from the servers. The QPIR problem has been treated by Song \emph{et al.} in the case of replicated servers, both without collusion and with all but one servers colluding. In this paper, the QPIR setting is extended to account for MDS-coded servers. The proposed protocol works for any [n,k]-MDS code and t-collusion with t = n - k. Similarly to the previous cases, the rates achieved are better than those known or conjectured in the classical counterparts.