A Matrix Convexity Approach to Some Celebrated Quantum Inequalities
classification
🧮 math-ph
math.MP
keywords
inequalitiesmatrixperspectivesquantumsomeadditionalalgebraicanalogue
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Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given using matrix perspectives of operator convex functions. A matrix analogue of Mar\'{e}chal's extended perspectives provides additional inequalities, including a $p+q\leq 1$ result of Lieb.
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