Quantum Private Information Retrieval from Coded and Colluding Servers
This work addresses quantum private information retrieval for distributed storage systems, offering incremental improvements over prior quantum protocols by incorporating coding and collusion resistance.
The paper tackles the problem of privately retrieving a classical file from quantum servers using maximum distance separable (MDS) coded storage and collusion, achieving rates better than classical counterparts and extending to locally repairable codes for higher retrieval rates.
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 receiving quantum information 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 maximum distance separable (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. Further, it is demonstrated how the protocol can adapted to achieve significantly higher retrieval rates from DSSs encoded with a locally repairable code (LRC) with disjoint repair groups, each of which is an MDS code.