  In a unified framework, we obtain two-sided estimates of the following
quantities of interest in quantum information theory:
  1.The minimum-error distinguishability of arbitrary ensembles of mixed
quantum states.
  2.The approximate reversibility of quantum dynamics in terms of entanglement
fidelity. (This is also referred to as "channel-adapted quantum error recovery"
when the reversed channel is the composition of an encoding operation and a
noise channel.)
  3.The maximum overlap between a bipartite pure quantum state and a bipartite
mixed state that may be achieved by applying a local quantum operation to one
part of the mixed state.
  4. The conditional min-entropy of bipartite quantum states.
  A refined version of the author's techniques [J. Math. Phys. 50, 032016] for
bounding the first quantity is employed to give two-sided estimates of the
remaining three quantities. Our primary tool is "small angle" initialization of
an abstract generalization of the iterative schemes for computing optimal
measurements and quantum error recoveries introduced by Jezek-Rehacek-Fiurasek
[Phys. Rev. A 65, 060301], Jezek-Fiurasek-Hradil [Phys. Rev. A 68, 012305], and
Reimpell-Werner [Phys. Rev. Lett 94, 080501].
