# Nonlocality Distillation and Quantum Voids

## TL;DR

This paper investigates nonlocality distillation, establishing a necessary condition for two-copy distillation, and demonstrates that certain quantum voids can be distilled to PR-boxes, revealing insights into post-quantum correlations and foundational principles.

## Contribution

It derives a necessary condition for nonlocality distillation from two copies and shows quantum voids can be distilled to PR-boxes, extending previous results.

## Key findings

- Quantum voids can be distilled to PR-boxes.
- A necessary condition for two-copy nonlocality distillation is established.
- Certain post-quantum correlations violate information principles.

## Abstract

Via nonlocality distillation, a number of copies of a given nonlocal correlation can be turned into a new correlation displaying a higher degree of nonlocality. Apart from its clear relevance in situations where nonlocality is a resource, distillation protocols also play an important role in the understanding of information-theoretical principles for quantum theory. Here, we derive a necessary condition for nonlocality distillation from two copies and apply it, among other results, to show that $1$D and $2$D quantum voids --faces of the nonlocal simplex set with no quantum realization-- can be distilled up to PR-boxes. With that, we generalize previous results in the literature. For instance, showing a broad class of post-quantum correlations that make communication complexity trivial and violate the information causality principle.