Non-locality of non-Abelian anyons

Abstract

Topological systems, such as fractional quantum Hall liquids, promise to successfully combat environmental decoherence while performing quantum computation. These highly correlated systems can support non-Abelian anyonic quasiparticles that can encode exotic entangled states. To reveal the non-local character of these encoded states we demonstrate the violation of suitable Bell inequalities. We provide an explicit recipe for the preparation, manipulation and measurement of the desired correlations for a large class of topological models. This proposal gives an operational measure of non-locality for anyonic states and it opens up the possibility to violate the Bell inequalities in quantum Hall liquids or spin lattices.

7 pages, 3 figures

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• Detecting Majorana bound states
• Decoding non-Abelian topological quantum memories
• A practical phase gate for producing Bell violations in Majorana wires
• Nonlocality as a Benchmark for Universal Quantum Computation in Ising Anyon Topological Quantum Computers
• Relational time in anyonic systems
• Demonstrating Entanglement by Testing Bell's Theorem in Majorana Wires
• Majorana bound states with chiral magnetic textures