Tailored two-photon correlation and fair-sampling: a cautionary tale

Abstract

We demonstrate an experimental test of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality which seemingly exhibits correlations beyond the limits imposed by quantum mechanics. Inspired by the idea of Fourier synthesis, we design analysers that measure specific superpositions of orbital angular momentum (OAM) states, such that when one analyser is rotated with respect to the other, the resulting coincidence curves are similar to a square-wave. Calculating the CHSH Bell parameter, $S$, from these curves result to values beyond the Tsirelson bound of $S_{QM}=2\sqrt{2}$. We obtain $S=3.99\pm 0.02$, implying almost perfect nonlocal Popescu-Rohrlich correlations. The "super-quantum" values of $S$ is only possible in our experiment because our experiment, subtly, does not comply with fair-sampling. The way our Bell test fails fair-sampling is not immediately obvious and requires knowledge of the states being measured. Our experiment highlights the caution needed in Bell-type experiments based on measurements within high-dimensional state spaces such as that of OAM, especially in the advent of device-independent quantum protocols.

to be published in New J Phys

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• High-Dimensional Single-Photon Quantum Gates: Concepts and Experiments
• Post-selection free spatial Bell state generation
• Quantum nonlocality with arbitrary limited detection efficiency
• Quantum nonlocality with arbitrary limited detection efficiency
• A dimensionality and purity measure for high-dimensional entangled states
• How post-selection affects device-independent claims under the fair sampling assumption
• Information Causality in the Quantum and Post-Quantum Regime
• Entanglement and Impropriety
• Coincidence postselection for genuine multipartite nonlocality: Causal diagrams and threshold efficiencies
• Extending the fair sampling assumption using causal diagrams