On the Capacity of Secure $K$-user Product Computation over a Quantum MAC
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916970507534336 |
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| author | Lu, Yuxiang Yao, Yuhang Jafar, Syed A. |
| author_facet | Lu, Yuxiang Yao, Yuhang Jafar, Syed A. |
| contents | Inspired by recent work by Christensen and Popovski on secure $2$-user product computation for finite-fields of prime-order over a quantum multiple access channel, the generalization to $K$ users and arbitrary finite fields is explored. Asymptotically optimal (capacity-achieving for large alphabet) schemes are proposed. Additionally, the capacity of modulo-$d$ ($d\geq 2$) secure $K$-sum computation is shown to be $2/K$ computations/qudit, generalizing a result of Nishimura and Kawachi beyond binary, and improving upon it for odd $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_20073 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Capacity of Secure $K$-user Product Computation over a Quantum MAC Lu, Yuxiang Yao, Yuhang Jafar, Syed A. Information Theory Inspired by recent work by Christensen and Popovski on secure $2$-user product computation for finite-fields of prime-order over a quantum multiple access channel, the generalization to $K$ users and arbitrary finite fields is explored. Asymptotically optimal (capacity-achieving for large alphabet) schemes are proposed. Additionally, the capacity of modulo-$d$ ($d\geq 2$) secure $K$-sum computation is shown to be $2/K$ computations/qudit, generalizing a result of Nishimura and Kawachi beyond binary, and improving upon it for odd $K$. |
| title | On the Capacity of Secure $K$-user Product Computation over a Quantum MAC |
| topic | Information Theory |
| url | https://arxiv.org/abs/2305.20073 |