Proposed optical test of Bell's inequalities not resting upon the fair sampling assumption

Emilio Santos

Guillaume Adenier

Marissa Giustina, Alexandra Mech, Sven Ramelow +9 more

Willem M. de Muynck, Hans Martens

Janis Strazdins

Fair sampling assumption is used in photonic tests of Bell inequalities. However, rigorous testing of this assumption is still to be performed. Here it is argued that without rigorous testing bias can be introduced that would mask indications of unfair sampling. For purpose of argument local realistic model for polarization entangled photons is outlined. According to model coincidence rate and correlation visibility are complementary.

Dominic William Berry, Hyunseok Jeong, Magdalena Stobińska +1 more

Almost all Bell inequality experiments to date have used postselection and therefore relied on the fair sampling assumption for their interpretation. The standard form of the fair sampling assumption is that the loss is independent of the measurement settings, so the ensemble of detected systems provides a fair statistical sample of the total ensemble. This is often assumed to be needed to interpret Bell inequality experiments as ruling out hidden-variable theories. Here we show that it is not necessary; the loss can depend on measurement settings, provided the detection efficiency factorizes as a function of the measurement settings and any hidden variable. This condition implies that Tsirelson's bound must be satisfied for entangled states. On the other hand, we show that it is possible for Tsirelson's bound to be violated while the Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality still holds for unentangled states, and present an experimentally feasible example.