---
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.'
author:
- 'S. G. A. Brito'
- 'M. G. M. Moreno'
- 'A. Rai'
- 'R. Chaves'
bibliography:
- 'Ref.bib'
title: Nonlocality Distillation and Quantum Voids
---

Introduction
============

Quantum correlations lie at the core of quantum enhanced information processing. Most prominently, entanglement [@RevModPhys.81.865] is a key ingredient in a variety of relevant applications, ranging from quantum computation [@nielsen2002quantum] to quantum metrology [@giovannetti2011advances] and quantum communication [@gisin2007quantum]. In the more recent years, another cornerstone 