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

## TL;DR

This paper derives general bounds for one-shot pure-state distillation in quantum resource theories, applicable to a wide range of theories with minimal assumptions, unifying and extending known results.

## Contribution

It introduces a unified framework for bounds on pure-state distillation applicable to general resource theories with minimal structural assumptions.

## Key findings

- Bounds expressed via the overlap function and robustness of resource
- Reproduces known results in coherence and entanglement theory
- Applicable to operations with limited resource generation

## Abstract

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. Known results in coherence and entanglement theory are reproduced in this more general framework.