Building on recent constructions of Quantum Cross Subspace Alignment (QCSA) codes, this work develops a coding scheme for QEXSTPIR, 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). The scheme is accordingly labeled QECSA, with the `E' indicating resilience to erased servers. The novelty of QECSA lies in achieving efficient $E$-straggler resilience on top of existing QCSA codes that already achieve $X$-secure storage, $T$-private queries, and distributed superdense coding gains for communication efficient decoding. The QECSA 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.

翻译：基于近期量子交叉子空间对准（QCSA）码的构造，本文提出了一种针对QEXSTPIR（即具有$X$-安全存储和$T$-私有查询的经典私有信息检索）的编码方案，该方案运行于量子多址接入信道之上，且能容忍任意不超过$E$个擦除服务器（亦称为无响应服务器或落后者）的集合。该方案相应地命名为QECSA，其中“E”表示对擦除服务器的鲁棒性。QECSA的创新在于：在现有QCSA码（已实现$X$-安全存储、$T$-私有查询以及用于通信高效解码的分布式超密编码增益）基础上，进一步实现了高效的$E$-落后者鲁棒性。QECSA码结构可广泛用于量子编码安全分布式计算等问题，此类问题同时要求安全性、落后者鲁棒性以及分布式超密编码增益。