Experimental demonstration of anyonic statistics with multiphoton entanglement

Particles in nature are usually distinguished according to their statistics in two categories: bosons and fermions. However, if one considers only two spatial dimensions statistical behaviour ranging from bosonic to fermionic is found. Particles exhibiting such a behaviour are called anyons. Our experimental demonstration of anyonic statistics is based on a particular two-dimensional model: the toric code proposed by Kitaev [1]. There, anyons arise as excitations that are generated by local operations. We show that for this model anyonic behaviour is revealed for as little as four qubits [2]. This enabled us to experimentally demonstrate anyonic statistics in a quantum simulation with four-photon entanglement. \newline [1] A.~Yu.~Kitaev, Ann. Phys. {\bf 303}, 2 (2003). \newline [2] J.~K.~Pachos {\emph{et al.}}, arXiv:0710.0895v2 [quant-ph] (2007).