Nonlocal correlations between the Canary Islands

Bell's inequality is the itch on the back of all believers in hidden variables. Based on only a few assumptions it states that some correlations in quantum mechanics can not be achieved by local realistic hidden variables theories. The correlations in hidden variables theories of that type have to fulfill an inequality, now named after John Bell, violations of which have been observed in experiment, thus hidden variables don't describe reality. But as always, the devil is in the details, and if one doesn't pay attention to the details, loopholes remain. For Bell's inequality, there are actually quite a few of them, and to date no experiment has managed to close them all.

The typical experiment for Bell's theorem makes use of a pair of photons (electrons), entangled in polarization (spin). The two particles are send in different directions and their polarizations are measured along different directions. The correlation among the pairs of repeated measurements is subject to Bell's inequality. (Or the more general CHSH inequality).

The maybe most obvious loophole, called the locality loophole, is that information could be locally communicated from one measurement to the other. Since information can maximally be transmitted by the speed of light this is the case if, for example, the second measurement is made with delay to the first, such that the second measurement is in the forward lightcone of the first. Another loophole is that the detector settings may possibly be correlated with the prepared state without any violations of locality if they are in the forward lightcone of the preparation. Since in this case the experimenter cannot actually set the detector as he wishes, it's called the freedom-of-choice loophole.

A case where both loopholes are present is depicted in the space-time image below. The event marked with "E" is the emission of the photos. The red lines are the worldlines of the entangled electrons or photons (in an optical fiber). "A" and "B" are the two measurements and "a" and "b" are the events at which the detector settings are chosen. Also in the image are the forward lightcones of the event "E" and "A".


So that's how you don't want to make your experiment if you're aiming to disprove locally realistic hidden variables. Instead, what you want to do is an experiment as in the second figure below, where not only the measurement events "A" and "B" are spacelike to each other (ie they are not in each other's lightcone), but also the events "a" and "b" at which the detector settings are chosen are spacelike to each other and to the emission of the photons.

Let us also recall that the lightcone is invariant under Lorentz-transformations and thus the statement whether two events are spacelike, timelike or lightlike to each other does not depend on the reference frame. If you manage to do it in one frame, it's good for all frames.

Looks simple enough in a diagram, less simple to actually do it: Entanglement is a fragile state and the speed of light, which is the maximum speed by which (hidden) information might travel is really, really fast. It helps if you let the entangled particles travel over long distances before you make the measurement, but then you have to be very careful in getting the timing right.

And that's exactly what a group of experimentalists around Anton Zeiliger did and published in November in their paper "Violation of local realism with freedom of choice" (arXiv version here). They closed for the first time both of the two above mentioned loopholes by choosing a setting that disabled communication between the measurement events as well as between the preparation of the photons and the choice of detector settings. The test was performed between two Canary Islands, La Palma and Tenerife.


[Image Source: Lonely Planet]
The polarization-entangled pairs of photons were produced in La Palma. One was guided to a transmitter telescope and sent over a distance of 144 km to Tenerife, where it was received by another telescope. The other photon made 6km of circles in a coiled optical fibre in La Palma. The detector settings in La Palma were chosen by a quantum random number generator 1.2 km away from the source, and in Tenerife by another similar but independent random number generator. The measurements violated Bell's inequality by more than 16 standard deviations.

What a beautiful experiment!

But if you're a believer in local realistic hidden variable theories, let me scratch your itch. You can't close the freedom-of-choice loophole in superdeterministic hidden variables theories with this method because there's no true randomness in that case. It doesn't matter where you locate your "random" generator, its outcome was determined arbitrarily long ago in the backward lightcone of the emission.