Majorana fermions and non-locality

TL;DR

This paper shows that Majorana fermions, despite limited operations, can be used to demonstrate non-local correlations in quantum experiments, highlighting their potential in quantum information processing.

Contribution

It demonstrates the feasibility of observing non-locality with Majorana fermions using only topologically protected operations, and establishes resource optimality for bipartite non-locality.

Findings

10 Majorana fermions are necessary and sufficient for bipartite non-locality.

Majorana fermions cannot demonstrate tripartite non-locality under current restrictions.

The proposed method is resource-optimal for non-locality demonstration.

Abstract

Localized Majorana fermions emerge in many topologically ordered systems and exhibit exchange statistics of Ising anyons. This enables noise-resistant implementation of a limited set of operations by braiding and fusing Majorana fermions. Unfortunately, these operations are incapable of implementing universal quantum computation. We show that, regardless of these limitations, Majorana fermions could be used to demonstrate non-locality (correlations incompatible with a local hidden variable theory) in experiments using only topologically protected operations. We also demonstrate that our proposal is optimal in terms of resources, with 10 Majorana fermions shown to be both necessary and sufficient for demonstrating bipartite non-locality. Furthermore, we identify severe restrictions on the possibility of tripartite non-locality. We comment on the potential of such entangled systems to be used in quantum information protocols.