Proposed all-versus-nothing violation of local realism in the Kitaev spin-lattice model

TL;DR

This paper demonstrates a fundamental quantum nonlocality in the Kitaev spin-lattice model by constructing a GHZ paradox, highlighting the purely quantum nature of fractional statistics and proposing an experimental test using anyonic interferometry.

Contribution

It introduces a novel GHZ paradox for the Kitaev model, revealing all-versus-nothing violations of local realism related to fractional statistics.

Findings

Fractional statistics in the Kitaev model is a purely quantum effect.

A GHZ paradox is constructed to show conflict with local realism.

An experimental scheme using anyonic interferometry is proposed.

Abstract

We investigate the nonlocal property of the fractional statistics in Kitaev's toric code model. To this end, we construct the Greenberger-Horne-Zeilinger paradox which builds a direct conflict between the statistics and local realism. It turns out that the fractional statistics in the model is purely a quantum effect and independent of any classical theory.We also discuss a feasible experimental scheme using anyonic interferometry to test this contradiction.