Variational representations related to Tsallis relative entropy

Abstract

We develop variational representations for the deformed logarithmic and exponential functions and use them to obtain variational representations related to the quantum Tsallis relative entropy. We extend Golden-Thompson's trace inequality to deformed exponentials with deformation parameter $q\in [0,1],$ thus complementing the second author's previous study of the cases with deformation parameter $q\in [1,2]$ or $q\in [2,3].$

References in corpus (9)

• User-friendly tail bounds for sums of random matrices
• Fundamental properties of Tsallis relative entropy
• A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity
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• A Stronger Subadditivity of Entropy
• From joint convexity of quantum relative entropy to a concavity theorem of Lieb
• Multivariate extensions of the Golden-Thompson inequality
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Cited by in corpus (1)

• Geometric properties for a class of deformed trace functions