A Coding Scheme for Straggler Resilient Quantum $X$-Secure $T$-Private Information Retrieval

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.