Characterisations of Matrix and Operator-Valued $\Phi$-Entropies, and Operator Efron-Stein Inequalities

Hao-Chung Cheng, Min-Hsiu Hsieh

We derive new characterisations of the matrix $\mathrm{\Phi }$-entropy functionals introduced in [Electron.~J.~Probab., 19(20): 1--30, 2014]. Notably, all known equivalent characterisati…