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In a unified framework, we obtain two-sided estimates of the followingquantities of interest in quantum information theory:  1.The minimum-error distinguishability of arbitrary ensembles of mixedquantum states.  2.The approximate reversibility of quantum dynamics in terms of entanglementfidelity. (This is also referred to as "channel-adapted quantum error recovery"when the reversed channel is the composition of an encoding operation and anoise channel.)  3.The maximum overlap between a bipartite pure quantum state and a bipartitemixed state that may be achieved by applying a local quantum operation to onepart 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] forbounding the first quantity is employed to give two-sided estimates of theremaining three quantities. Our primary tool is "small angle" initialization ofan abstract generalization of the iterative schemes for computing optimalmeasurements and quantum error recoveries introduced by Jezek-Rehacek-Fiurasek[Phys. Rev. A 65, 060301], Jezek-Fiurasek-Hradil [Phys. Rev. A 68, 012305], andReimpell-Werner [Phys. Rev. Lett 94, 080501].

journal of mathematical physics

Two-sided bounds on minimum-error quantum measurement, on the  reversibility of quantum dynamics, and on the maximum overlap problem using  directional iterates