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

Understand

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.