Building on recent constructions of Quantum Cross Subspace Alignment (QCSA) codes, this work develops a coding scheme for QEBXSTPIR, i.e., classical private information retrieval with $X$-secure storage and $T$-private queries, over a quantum multiple access channel, that is resilient to any set of up to $E$ erased servers (equivalently known as unresponsive servers, or stragglers) together with any set of up to $B$ Byzantine servers. The scheme is accordingly labeled QEBCSA, with the `E' and `B' indicating resilience to erased and Byzantine servers respectively. The QEBCSA code structure may be broadly useful for problems such as quantum coded secure distributed computation, where security, straggler resilience, and distributed superdense coding gains are simultaneously required. The $X$-security property is further exploited to improve the communication rate when $\epsilon$-error decoding is allowed.

翻译：基于近期量子交叉子空间对齐（QCSA）码的构造，本文针对量子多址接入信道上的经典隐私信息检索问题（具有$X$-安全存储与$T$-隐私查询，且可容忍任意至多$E$个擦除服务器（亦称无响应服务器或掉队服务器）及任意至多$B$个拜占庭服务器），提出了一种编码方案。该方案相应地命名为QEBCSA，其中“E”与“B”分别表示对擦除服务器与拜占庭服务器的鲁棒性。QEBCSA码结构可广泛适用于量子编码安全分布式计算等问题，这类问题同时要求安全性、掉队服务器鲁棒性以及分布式超密编码增益。此外，本文进一步利用$X$-安全特性，在允许$\epsilon$-误差解码时提升通信速率。