Monotonicity of optimized quantum $f$-divergence

Understand

Optimized quantum $f$-divergence was first introduced by Wilde in \cite{Wil18}.

• Wilde raised the question of whether the monotonicity of optimized quantum $f$-divergence can be generalized to maps that are not quantum channels.
• We answer this question by generalizing the monotonicity of optimized quantum $f$-divergences to positive trace preserving maps satisfying a Schwarz inequality.