Title: Experimental GHZ Entanglement beyond Qubits,
Abstract: The Greenberger-Horne-Zeilinger (GHZ) argument provides an all-or-nothing
contradiction between quantum mechanics and local-realistic theories. In its
original formulation, GHZ investigated three and four particles entangled in
two dimensions only. Very recently, higher dimensional contradictions
especially in three dimensions and three particles have been discovered but it
has remained unclear how to produce such states. In this article we
experimentally show how to generate a three-dimensional GHZ state from
two-photon orbital-angular-momentum entanglement. The first suggestion for a
setup which generates three-dimensional GHZ entanglement from these entangled
pairs came from using the computer algorithm Melvin. The procedure employs
novel concepts significantly beyond the qubit case. Our experiment opens up the
possibility of a truly high-dimensional test of the GHZ-contradiction which,
interestingly, employs non-Hermitian operators.