🤖 AI Summary
This work addresses communication-efficient quantum private information retrieval (QPIR) in multi-server-to-single-user quantum networks. We propose the first fault-tolerant Q-E-B-MDS-X-TPIR protocol, which guarantees X-secure data storage and T-private queries under MDS-coded distributed storage, while tolerating up to E unresponsive and B Byzantine servers. Methodologically, we introduce a novel integration of modified cross-subspace alignment (MCSA) codes with CSS-based quantum error-correcting codes: interference terms are aligned within a stable code subspace, while the target computation is embedded into an error-correcting subspace; this synergistic design is further enhanced by quantum superdense coding to boost communication efficiency. Compared to classical baselines, our protocol achieves significant superdense coding gains and unifies multiple state-of-the-art quantum PIR settings. To the best of our knowledge, it is the first coding framework for quantum fault-tolerant distributed computing that simultaneously ensures high communication efficiency, strong security guarantees (X-security and T-privacy), and robust fault tolerance.
📝 Abstract
A communication-efficient protocol is introduced over a many-to-one quantum network for Q-E-B-MDS-X-TPIR, i.e., quantum private information retrieval with MDS-X-secure storage and T-private queries. The protocol is resilient to any set of up to E unresponsive servers (erased servers or stragglers) and any set of up to B Byzantine servers. The underlying coding scheme incorporates an enhanced version of a Cross Subspace Alignment (CSA) code, namely a Modified CSA (MCSA) code, into the framework of CSS codes. The error-correcting capabilities of CSS codes are leveraged to encode the dimensions that carry desired computation results from the MCSA code into the error space of the CSS code, while the undesired interference terms are aligned into the stabilized code space. The challenge is to do this efficiently while also correcting quantum erasures and Byzantine errors. The protocol achieves superdense coding gain over comparable classical baselines for Q-E-B-MDS-X-TPIR, recovers as special cases the state of art results for various other quantum PIR settings previously studied in the literature, and paves the way for applications in quantum coded distributed computation, where CSA code structures are important for communication efficiency, while security and resilience to stragglers and Byzantine servers are critical.