High-Rate Quantum Private Information Retrieval with Weakly Self-Dual Star Product Codes
This work addresses the challenge of secure data retrieval in distributed quantum systems, offering improved privacy and efficiency for applications like cloud storage, though it is incremental as it builds on existing QPIR frameworks.
The paper tackles the problem of quantum private information retrieval (QPIR) from coded servers with collusion, achieving high retrieval rates for any number of colluding servers up to n-k, outperforming classical and prior quantum schemes.
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 et al. in the case of replicated servers, both with and without collusion. QPIR over $[n,k]$ maximum distance separable (MDS) coded servers was recently considered 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 retrieval rate. In this paper, the QPIR setting is extended to allow for retrieval with high 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 known or conjectured in the classical counterparts, as well as those of the previously proposed coded and colluding QPIR schemes. This is enabled by considering the stabilizer formalism and weakly self-dual generalized Reed--Solomon (GRS) star product codes.