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

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 $\delta \ge 0$ 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.

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Cited by in corpus (7)

• One-Shot Manipulation of Dynamical Quantum Resources
• Virtual quantum resource distillation
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Every quantum helps: Operational advantage of quantum resources beyond convexity
• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
• Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity
• Cone-Restricted Information Theory