Some applications of matrix inequalities in Rényi entropy

The R{é}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{é}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital importance. Another important quantity is R{é}nyi relative entropy on which R{é}nyi generalization of the conditional entropy, and mutual information are defined based. Thus, finding lower bound for R{é}nyi relative entropy is our goal in this paper. We use matrix inequalities to prove new bounds on the entropy of type $β$, R{é}nyi entropy.

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