Quantum probabilistic sampling of multipartite 60-qubit Bell-inequality violations

We show that violation of genuine multipartite Bell inequalities can be obtained with sampled, probabilistic phase-space methods. These genuine Bell violations cannot be replicated if any part of the system is described by a local hidden variable theory. The Bell violations are simulated probabilistically using quantum phase-space representations. We treat mesoscopically large Greenberger-Horne-Zeilinger (GHZ) states having up to 60 qubits, using both a multipartite SU(2)-Q representation and the positive-P representation. Surprisingly, we find that sampling with phase-space distributions can be exponentially faster than experiment. This is due to the classical parallelism inherent in the simulation of quantum measurements using phase-space methods. Our probabilistic sampling method predicts a contradiction with local realism of 'Schroedinger-cat' states that can be realized as a GHZ spin state, either in ion traps or with photonic qubits. We also present a quantum simulation of the observed superdecoherence of the ion-trap 'cat' state, using a phenomenological noise model.