Quantum Cross Subspace Alignment Codes via the $N$-sum Box Abstraction
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908557136363520 |
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| author | Lu, Yuxiang Jafar, Syed Ali |
| author_facet | Lu, Yuxiang Jafar, Syed Ali |
| contents | 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) \emph{over-the-air}. Applications include Quantum PIR with secure and MDS-coded storage, as well as Quantum SDBMM. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14676 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum Cross Subspace Alignment Codes via the $N$-sum Box Abstraction Lu, Yuxiang Jafar, Syed Ali Information Theory 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) \emph{over-the-air}. Applications include Quantum PIR with secure and MDS-coded storage, as well as Quantum SDBMM. |
| title | Quantum Cross Subspace Alignment Codes via the $N$-sum Box Abstraction |
| topic | Information Theory |
| url | https://arxiv.org/abs/2304.14676 |