Quantum $X$-Secure $T$-Private Information Retrieval From MDS Coded Storage With Unresponsive and Byzantine Servers

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.

References in corpus (9)

• How to share a quantum secret
• Private Information Retrieval from Coded Databases with Colluding Servers
• Quantum Error Correction
• Secure Quantum Network Code without Classical Communication
• Unified Approach to Secret Sharing and Symmetric Private Information Retrieval with Colluding Servers in Quantum Systems
• The Capacity of Classical Summation over a Quantum MAC with Arbitrarily Distributed Inputs and Entanglements
• Quantum Cross Subspace Alignment Codes via the $N$-sum Box Abstraction
• On the Capacity of Secure $K$-user Product Computation over a Quantum MAC
• Private Product Computation using Quantum Entanglement