On maximization of measured $f$-divergence between a given pair of quantum states

Understand

This paper deals with maximization of classical $f$-divergence between the distributions of a measurement outputs of a given pair of quantum states.

• $f$-divergence $D_{f}$ between the probability density functions $p_{1}$ and $p_{2}$ over a discrete set is defined as $D_{f}( p_{1}||p_{2}) :=\sum_{x}p_{2}(x) f\left(p_{1}(x)/p_{2}( x) \right) $.
• For example, Kullback-Leibler divergence and Renyi type relative entropy are well-known examples with good operational meanings.
• Thus, finding the maximal value $D_{f}^{\min}$ of measured measured $f$-divergence is also an interesting question.