We consider the problems arising from the presence of Byzantine servers in a quantum private information retrieval (QPIR) setting. This is the first work to precisely define what the capabilities of Byzantine servers could be in a QPIR context. We show that quantum Byzantine servers have more capabilities than their classical counterparts due to the possibilities created by quantum encoding procedures. We focus on quantum Byzantine servers that can apply any reversible operation on their individual qudits. In this case, Byzantine servers can generate any error, i.e., this covers \emph{all} possible single qudit operations that can be applied by Byzantine servers on their qudits. We design a scheme based on cross-subspace alignment (CSA) and we show that this scheme achieves superdense coding gain in some cases.

翻译：本文考虑了量子私有信息检索（QPIR）场景中拜占庭服务器存在所引发的问题。这是首次精确定义拜占庭服务器在量子私有信息检索上下文中可能具备的能力。研究表明，由于量子编码过程带来的可能性，量子拜占庭服务器比经典拜占庭服务器具有更强的能力。我们重点关注能够对其各自量子比特施加任意可逆操作的量子拜占庭服务器。在这种情况下，拜占庭服务器可以产生任意错误，即这涵盖了拜占庭服务器可对其量子比特施加的\emph{所有}可能的单个量子比特操作。我们设计了一种基于子空间交叉对齐（CSA）的方案，并证明该方案在某些情况下可实现超密编码增益。