On Strong Converse Theorems for Quantum Hypothesis Testing and Channel Coding
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914721546895360 |
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| author | Cheng, Hao-Chung Gao, Li |
| author_facet | Cheng, Hao-Chung Gao, Li |
| contents | Strong converse theorems refer to the study of impossibility results in information theory. In particular, Mosonyi and Ogawa established a one-shot strong converse bound for quantum hypothesis testing [Comm. Math. Phys, 334(3), 2014], which servers as a primitive tool for establishing a variety of tight strong converse theorems in quantum information theory. In this short note, we demonstrate an alternative one-line proof for this bound via the variational expression of measured Rényi divergences [Lett. Math. Phys, 107(12), 2017]. Then, we show that the variational expression is a direct consequence of Hölder's inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13584 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Strong Converse Theorems for Quantum Hypothesis Testing and Channel Coding Cheng, Hao-Chung Gao, Li Quantum Physics Mathematical Physics Strong converse theorems refer to the study of impossibility results in information theory. In particular, Mosonyi and Ogawa established a one-shot strong converse bound for quantum hypothesis testing [Comm. Math. Phys, 334(3), 2014], which servers as a primitive tool for establishing a variety of tight strong converse theorems in quantum information theory. In this short note, we demonstrate an alternative one-line proof for this bound via the variational expression of measured Rényi divergences [Lett. Math. Phys, 107(12), 2017]. Then, we show that the variational expression is a direct consequence of Hölder's inequality. |
| title | On Strong Converse Theorems for Quantum Hypothesis Testing and Channel Coding |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2403.13584 |