Doubly minimized sandwiched Renyi mutual information: Properties and operational interpretation from strong converse exponent
| Autor: | Burri, Laura |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we deepen the study of properties of the doubly minimized sandwiched Renyi mutual information, which is defined as the minimization of the sandwiched divergence of order $\alpha$ of a fixed bipartite state relative to any product state. In particular, we prove a novel duality relation for $\alpha\in [\frac{2}{3},\infty]$ by employing Sion's minimax theorem, and we prove additivity for $\alpha\in [\frac{2}{3},\infty]$. Previously, additivity was only known for $\alpha\in [1,\infty]$, but has been conjectured for $\alpha\in [\frac{1}{2},\infty]$. Furthermore, we show that the doubly minimized sandwiched Renyi mutual information of order $\alpha\in [1,\infty]$ attains operational meaning in the context of binary quantum state discrimination as it is linked to certain strong converse exponents. Comment: 17+27 pages, 1 figure, 2 tables, see similar work: arXiv:2406.01699 (see Section 1 for detailed information) |
| Databáze: | arXiv |
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