  We prove number of quantitative stability bounds for the cases of equality in
Petz's monotonicity theorem for quasi-relative entropies defined in terms of an
operator monotone decreasing functions. Included in our results is a bound in
terms of the Petz recovery map, but we obtain more general results. The present
treatment is entirely elementary and developed in the context of finite
dimensional von Neumann algebras where the results are already non-trivial and
of interest in quantum information theory.
