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 this paper, the QPIR setting is extended to account for more flexible collusion of servers satisfying $t < n-k+1$. 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.

翻译：在古典私人信息检索(PIR)设置中,用户希望从数据库或分布式存储系统检索文件,但不向持有数据的服务器透露文件身份。在量子 PIR(QPIR)设置中,用户通过接收服务器的量子信息私下检索一个古典文件。 Song等人在复制服务器的情况下处理QPIR问题,无论是否相互串通。Allaix等人最近审议了$[n,k]$的最大距离分解(MDS)编码服务器的QPIR,但这种串通基本上限于$t=n-k$服务器。在本文中,QPIR设置扩大到说明满足 $t < n-k+1$的服务器更灵活的串通。与以前的案件一样,所实现的费率比古典对口中已知或输入的要好,也比先前提议的编码和串联的QPIR(MDS)方案更好,这可以通过考虑稳定器形式和弱力的自我通用Reed-SgR(S)产品编码来实现。