Additivity and chain rules for quantum entropies via multi-index Schatten norms
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917333969141760 |
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| author | Fawzi, Omar Kochanowski, Jan Rouzé, Cambyse Van Himbeeck, Thomas |
| author_facet | Fawzi, Omar Kochanowski, Jan Rouzé, Cambyse Van Himbeeck, Thomas |
| contents | The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minimum output entropy of a channel, often plays a crucial role. A fundamental question in quantum information and cryptography is whether the minimum output entropy remains additive under the tensor product of channels. Here, we establish a general additivity statement for the optimized sandwiched Rényi entropy of quantum channels. For that, we generalize the results of [Devetak, Junge, King, Ruskai, CMP 2006] to multi-index Schatten norms. As an application, we strengthen the additivity statement of [Van Himbeeck and Brown, 2025] thus allowing the analysis of time-adaptive quantum cryptographic protocols. In addition, we establish chain rules for Rényi conditional entropies that are similar to the ones used for the generalized entropy accumulation theorem of [Metger, Fawzi, Sutter, Renner, CMP 2024]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Additivity and chain rules for quantum entropies via multi-index Schatten norms Fawzi, Omar Kochanowski, Jan Rouzé, Cambyse Van Himbeeck, Thomas Quantum Physics Mathematical Physics Functional Analysis Operator Algebras The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minimum output entropy of a channel, often plays a crucial role. A fundamental question in quantum information and cryptography is whether the minimum output entropy remains additive under the tensor product of channels. Here, we establish a general additivity statement for the optimized sandwiched Rényi entropy of quantum channels. For that, we generalize the results of [Devetak, Junge, King, Ruskai, CMP 2006] to multi-index Schatten norms. As an application, we strengthen the additivity statement of [Van Himbeeck and Brown, 2025] thus allowing the analysis of time-adaptive quantum cryptographic protocols. In addition, we establish chain rules for Rényi conditional entropies that are similar to the ones used for the generalized entropy accumulation theorem of [Metger, Fawzi, Sutter, Renner, CMP 2024]. |
| title | Additivity and chain rules for quantum entropies via multi-index Schatten norms |
| topic | Quantum Physics Mathematical Physics Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2502.01611 |