Recoverability for optimized quantum f-divergences

The optimized quantum $f$-divergences form a family of distinguishability measures that includes the relative entropy and sandwiched R\'enyi quasi-entropy as special cases. In this paper, we establish physically meaningful refinements data-processing inequality for $f$-divergence. particular, state absolute difference between $f$-divergence its channel-processed version is an upper bound on how well one can recover acted upon by channel, whenever recovery channel taken to be rotated Petz channel. Not only do these results lead entropy, but they also have implications perfect reversibility (i.e., sufficiency) $f$-divergences. Along way, improve previous standard $f$-divergence, established in recent work Carlen Vershynina [arXiv:1710.02409, arXiv:1710.08080]. Finally, extend definition inequality, all our recoverability general von Neumann algebraic setting, so employed physical settings beyond those confined most common finite-dimensional setting interest information theory.