Partial majorization and Schur concave functions on the sets of quantum and classical states

M. E. Shirokov

We construct for a Schur concave function $f$ on the set of quantum states a tight upper bound on the difference $f(\ddot{I})-f(\ddot{I}ƒ)$ for a quantum state $\ddot{I}$ with finite $f(\ddot{I})$ and any…