A Matrix Convexity Approach to Some Celebrated Quantum Inequalities

Details A Matrix Convexity Approach to Some Celebrated Quantum Inequalities A Matrix Convexity Approach to Some Celebrated Quantum Inequalities

2008-02-10

arxiv.org/abs/0802.1234v1

Physics

Mathematical Physics

8 pages

Scientific paper

10.1073/pnas.0807965106

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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