A Matrix Convexity Approach to Some Celebrated Quantum Inequalities
arXiv:0802.1234 · doi:10.1073/pnas.0807965106
Abstract
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 Maréchal's extended perspectives provides additional inequalities, including a result of Lieb.
8 pages