Closing the loopholes

David Wick

Serge Massar

It is shown that the detection loophole that arises when trying to rule out local realistic theories as alternatives for quantum mechanics can be closed if the detection efficiency $\ensuremath{\eta}>~{\mathrm{Cd}}^{3/4}{2}^{\ensuremath{-}0.0035d}$ where d is the dimension of the bipartite entangled system and C is a positive constant. Furthermore it is argued that such an exponential decrease of the detector efficiency required to close the detection loophole is almost optimal. This optimality argument is based on a close connection that exists between closing the detection loophole and the amount of classical communication required to simulate quantum correlations when the detectors are perfect.

Thomas Scheidl, Rupert Ursin, Johannes Kofler +8 more

Bell's theorem shows that local realistic theories place strong restrictions on observable correlations between different systems, giving rise to Bell's inequality which can be violated in experiments using entangled quantum states. Bell's theorem is based on the assumptions of realism, locality, and the freedom to choose between measurement settings. In experimental tests, "loopholes" arise which allow observed violations to still be explained by local realistic theories. Violating Bell's inequality while simultaneously closing all such loopholes is one of the most significant still open challenges in fundamental physics today. In this paper, we present an experiment that violates Bell's inequality while simultaneously closing the locality loophole and addressing the freedom-of-choice loophole, also closing the latter within a reasonable set of assumptions. We also explain that the locality and freedom-of-choice loopholes can be closed only within nondeterminism, i.e., in the context of stochastic local realism.

Richard David Gill

In this note, I analyze the data generated by M. Fodje's (2013) simulation programs "epr-simple" and "epr-clocked". They were written in Python and published on Github. Inspection of the program descriptions shows that they make use of the detection-loophole and the coincidence-loophole respectively. I evaluate them with appropriate modified Bell-CHSH type inequalities: the Larsson detection-loophole adjusted CHSH, and the Larsson-Gill coincidence-loophole adjusted CHSH (NB: its correctness is conjecture, we do not have proof). The experimental efficiencies turn out to be approximately eta = 81% (close to optimal) and gamma = 55% (far from optimal). The observed values of CHSH are, as they should be, within the appropriately adjusted bounds. Fodjes' detection-loophole model turns out to be very, very close to Pearle's famous 1970 model, so the efficiency is close to optimal. The model has the same defect as Pearle's: the joint detection rates exhibit signaling. Fodje's coincidence-loophole model is actually a clever modification of his detection-loophole model. Because of this, however, it cannot lead to optimal efficiency.

Owain P. H. Vaughan