Doubly minimized Petz Renyi mutual information: Properties and operational interpretation from direct exponent
| Autor: | Burri, Laura |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The doubly minimized Petz Renyi mutual information of order $\alpha$ is defined as the minimization of the Petz divergence of order $\alpha$ of a fixed bipartite quantum state relative to any product state. In this work, we establish several properties of this type of Renyi mutual information, including its additivity for $\alpha\in [1/2,2]$. As an application, we show that the direct exponent of certain binary quantum state discrimination problems is determined by the doubly minimized Petz Renyi mutual information of order $\alpha\in (1/2,1)$. This provides an operational interpretation of this type of Renyi mutual information, and generalizes a previous result for classical probability distributions to the quantum setting. Comment: 19+30 pages, 2 figures, 2 tables |
| Databáze: | arXiv |
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