Doubly minimized Petz Renyi mutual information: Properties and operational interpretation from direct exponent
<|reference_start|>Doubly minimized Petz Renyi mutual information: Properties and operational interpretation from direct exponent: 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.<|reference_end|>
@article{burri2024doubly,
    title={Doubly minimized Petz Renyi mutual information: Properties and
  operational interpretation from direct exponent},
    author={Laura Burri},
    journal={arXiv preprint arXiv:2406.01699},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.01699},
    primaryClass={quant-ph cs.IT math.IT}
}