Quantum Private Information Retrieval from Coded and Colluding Servers
share
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 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. It is also demonstrated how the retrieval rates can be significantly improved by using locally repairable codes (LRCs) consisting of disjoint repair groups, each of which is an MDS code. Finally, numerical results based on an implementation on an IBM quantum computer are presented, showing that even the current stability of quantum computers gives satisfactory results.
READ FULL TEXT