On testing objective local theories by using Greenberger-Horne-Zeilinger states

Boon Leong Lan

Herbert Joseph Bernstein

Dong-Ling Deng, Chunfeng Wu, Jing‐Ling Chen +1 more

We propose a scheme to test the Greenberger-Horne-Zeilinger paradox based on braidings of non-Abelian anyons, which are exotic quasiparticle excitations of topological states of matter. Because topological ordered states are robust against local perturbations, this scheme is in some sense "fault-tolerant" and might close the detection inefficiency loophole problem in previous experimental tests of the Greenberger-Horne-Zeilinger paradox. In turn, the construction of the Greenberger-Horne-Zeilinger paradox reveals the nonlocal property of non-Abelian anyons. Our results indicate that the non-Abelian fractional statistics is a pure quantum effect and cannot be described by local realistic theories. Finally, we present a possible experimental implementation of the scheme based on the anyonic interferometry technologies.

Christopher C. Gerry, Adil Benmoussa, K. Elalouani

An optical realization of the Greenberger, Horne, Zeilinger (GHZ) state is proposed for testing local realistic theories. The optical GHZ states in this case are three-mode entangled coherent states and the relevant observable used to perform tests of quantum mechanics against local realistic theories is photon number parity. The amplitudes of the coherent states need to be mesoscopic if significant losses are involved but may be macroscopic if losses are minimal. A method is proposed for generating the required GHZ state that amounts to an extension of a proposal previously discussed (C.C. Gerry, Phys. Rev. A 59 4095 (1999)) for generating macroscopic superposition states of travelling wave fields.

J. Edwards

J. Edwards, L. E. Ballentine