Simple Bounds for One-shot Pure-State Distillation in General Resource Theories

Understand

We present bounds for distilling many copies of a pure state from an arbitrary initial state in a general quantum resource theory.

• Our bounds apply to operations that are able to generate no more than a $\delta$ amount of resource, where $\delta \geq 0$ is a given parameter.
• To maximize applicability of our upper bound, we assume little structure on the set of free states under consideration besides a weak form of superadditivity of the function $G_{min}(\rho)$, which measures the overlap between $\rho$ and the set of free states.
• Our bounds are given in terms of this function and the robustness of resource.