Hardy's test versus the Clauser-Horne-Shimony-Holt test of quantum nonlocality: Fundamental and practical aspects

We compare two different tests of quantum nonlocality, both in theoretical terms and with respect to a possible implementation in a mesoscopic circuit: Hardy’s test [L. Hardy, Phys. Rev. Lett. 68, 2981 (1992)] and the Clauser-Horne-Shimony-Holt (CHSH) test, the latter including a recently discovered inequality relevant for experiments with three possible outcomes [D. Collins and N. Gisin, J. Phys. A 37, 1775 (2004)]. We clarify the geometry of the correlations defined by Hardy’s equations with respect to the polytope of causal correlations, and show that these equations generalize to the CHSH inequality if the slightest imperfections in the setup need to be taken into account. We propose a mesoscopic circuit consisting of two interacting Mach-Zehnder interferometers in a Hall bar system for which both Hardy’s test and the CHSH test can be realized with a simple change of gate voltages, and evaluate the robustness of the two tests in the case of fluctuating experimental parameters. The proposed setup is remarkably robust and should work for fluctuations of beam splitter angles or phases up to the order of 1 radian, or single particle loss rates up to about 15%.