Rényi-Holevo inequality from $α$-$z$-Rényi relative entropies
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913146757709824 |
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| author | Bussandri, Diego G. Rajchel-Mieldzioć, Grzegorz Lamberti, Pedro W. Życzkowski, Karol |
| author_facet | Bussandri, Diego G. Rajchel-Mieldzioć, Grzegorz Lamberti, Pedro W. Życzkowski, Karol |
| contents | We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures. Through the introduction of the $α$-$z$-Rényi relative entropies, which comprise known relevant quantities such as the Rényi relative entropy and the sandwiched Rényi relative entropy, we establish the Holevo-Rényi inequality. This result leads to a quantum bound for the $α$-mutual information, suggesting new insights into communication channel performance and the fundamental limits for reliability functions in memoryless multi-letter communication channels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_04539 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rényi-Holevo inequality from $α$-$z$-Rényi relative entropies Bussandri, Diego G. Rajchel-Mieldzioć, Grzegorz Lamberti, Pedro W. Życzkowski, Karol Quantum Physics We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures. Through the introduction of the $α$-$z$-Rényi relative entropies, which comprise known relevant quantities such as the Rényi relative entropy and the sandwiched Rényi relative entropy, we establish the Holevo-Rényi inequality. This result leads to a quantum bound for the $α$-mutual information, suggesting new insights into communication channel performance and the fundamental limits for reliability functions in memoryless multi-letter communication channels. |
| title | Rényi-Holevo inequality from $α$-$z$-Rényi relative entropies |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2309.04539 |