A Matrix Convexity Approach to Some Celebrated Quantum Inequalities

Understand

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.