Why Bell's Inequalities Fail to Comply with Experiment

Jacquiline Romero, D Giovannini, D S Tasca +2 more

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 . We obtain S = 3.99 ± 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.

Alain Aspect

Jacquiline Romero, Giovannini, D, Tasca, D S +2 more

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 . We obtain S = 3.99 ± 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.

Alain Aspect, Philippe Grangier

Alain Aspect

Intuitively, violations of Bell's inequality make no sense because one cannot violate a mathematical relationship unless it is wrong, or has been misused. However, the rotating polarizer experiment has been argued to provide such violations, and it is asserted this requires non-locality. It is shown here that at least one form of the inequality is violated because the results violate a condition used in deriving the inequality. The problem arises from mixed frames of reference being utilized, and if an external reference frame is employed, such as a polarized source, the inequality should be complied with. This could be verified by experiment. It is also important to resolve this as entanglement is to be potentially involved equipment such as quantum computing. Correct understanding may assist in such design.