On distinguishability distillation and dilution exponents

TL;DR

This paper introduces error and strong converse exponents for distinguishability distillation and dilution, providing methods to evaluate and relate these exponents within the resource theory of asymmetric distinguishability.

Contribution

It defines new exponents for distinguishability tasks, shows they can be computed via semi-definite programming, and establishes their properties and bounds using Renyi relative entropies.

Findings

Exponents can be evaluated by semi-definite programming.

Properties and bounds of exponents are established.

Relations between different exponents are derived.

Abstract

In this note, I define error exponents and strong converse exponents for the tasks of distinguishability distillation and dilution. These are counterparts to the one-shot distillable distinguishability and the one-shot distinguishability cost, as previously defined in the resource theory of asymmetric distinguishability. I show that they can be evaluated by semi-definite programming, establish a number of their properties, bound them using Renyi relative entropies, and relate them to each other.