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 the quantum encoding procedure. We focus on quantum Byzantine servers that can apply any reversible operations on their individual qudits. In this case, the Byzantine servers can generate any error, i.e., this covers \emph{all} possible single qudit operations that can be done by the Byzantine servers on their qudits. We design a scheme that is resilient to these kinds of manipulations. We show that the scheme designed achieves superdense coding gain in all cases, i.e., $R_Q= \max \left\{0,\min\left\{1,2\left(1-\frac{X+T+2B}{N}\right)\right\}\right\}$.

翻译：我们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环境中可能具备的能力。研究表明，由于量子编码过程所带来的可能性，量子拜占庭服务器比经典拜占庭服务器拥有更强的能力。我们重点关注能够对其单个量子比特（qudit）施加任意可逆操作的量子拜占庭服务器。在此情况下，拜占庭服务器能够生成任意错误，即涵盖拜占庭服务器可对其量子比特施加的所有可能的单量子比特操作。我们设计了一种能够抵御此类操纵的方案。研究证明，该方案在所有情况下均能实现超密编码增益，即$R_Q= \max \left\{0,\min\left\{1,2\left(1-\frac{X+T+2B}{N}\right)\right\}\right\}$。