Quantum Cross Subspace Alignment Codes via the N-sum Box Abstraction

Cross-subspace alignment (CSA) codes are used in various private information retrieval (PIR) schemes (e.g., with secure storage) and in secure distributed batch matrix multiplication (SDBMM). Using a recently developed N -sum box abstraction of a quantum multiple-access channel (QMAC), we translate...

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Bibliographic Details
Published inConference record - Asilomar Conference on Signals, Systems, & Computers pp. 670 - 674
Main Authors Lu, Yuxiang, Jafar, Syed A.
Format Conference Proceeding
LanguageEnglish
Published IEEE 29.10.2023
Subjects
Codes
Computers
Encoding
Information retrieval
Quantum entanglement
Secure storage
Wireless networks
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Summary:Cross-subspace alignment (CSA) codes are used in various private information retrieval (PIR) schemes (e.g., with secure storage) and in secure distributed batch matrix multiplication (SDBMM). Using a recently developed N -sum box abstraction of a quantum multiple-access channel (QMAC), we translate CSA schemes over classical multiple-access channels into efficient quantum CSA schemes over a QMAC, achieving maximal superdense coding gain. Because of the N -sum box abstraction, the underlying problem of coding to exploit quantum entanglements for CSA schemes, becomes conceptually equivalent to that of designing a channel matrix for a MIMO MAC subject to given structural constraints imposed by the N -sum box abstraction, such that the resulting MIMO MAC is able to implement the functionality of a CSA scheme (encoding/decoding) over-the-air. Applications include Quantum PIR with secure and MDS-coded storage, as well as Quantum SDBMM.
ISSN:2576-2303
DOI:10.1109/IEEECONF59524.2023.10477050