# Quantifying quantum resources with conic programming

## TL;DR

This paper demonstrates how conic programming can be used to quantify quantum resources by linking robustness measures to performance in discrimination tasks, with applications to various resource theories.

## Contribution

It introduces a general method to interpret robustness measures as performance quantifiers in discrimination tasks using conic programming.

## Key findings

- Robustness measures can be seen as quantifiers of outperformance in discrimination tasks.
- The technique applies to resource theories like joint measurability, POVMs, and Schmidt number.
- Conic programming provides a unified framework for resource quantification.

## Abstract

Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and incompatibility of quantum measurements. Given a certain state or measurement, one can ask whether there is a task in which it performs better than any resourceless state or measurement. Using conic programming, we prove that any general robustness measure (with respect to a convex set of free states or measurements) can be seen as a quantifier of such outperformance in some discrimination task. We apply the technique to various examples, e.g. joint measurability, POVMs simulable by projective measurements, and state assemblages preparable with a given Schmidt number.