There are a number of experimental problems or “loopholes” that may affect the validity of results in Bell test experiments conducted with the type of apparatus we just described. The main challenge relates to the low detection efficiency of optical systems, and the way in which it affects the “fair sampling” of coincidences that could bias the results in favor of quantum entanglement rather than local hidden variables.
We must recognize that the detection efficiency of our optical system is much lower than the ~70% quantum efficiency of the SPADs. A huge number of photons are lost along the way, especially within the polarizers, lenses, and filters, as well as when photons cross the interface between these optical components and air. Our detection efficiency with the setup of Figure 147 is probably around 5%. The best optical experiments conducted with high-quality components and using fiber-optics may approach a detection efficiency of up to 35%.
Much theoretical work has been done to determine the effect of low-efficiency detection, and the consensus is that a sufficiently large sample of detected pairs is representative of the pairs emitted, irrespective of the efficiency. Unfortunately, there is no way to experimentally test whether a given experiment does fair sampling, and that is why we recommend extending the sampling time to collect at least 1,000 coincident counts for case 1.
There are some Bell test experiments that have been performed using two ions rather than photons, which allowed the detection efficiency to be 100%, thus closing the fair sampling loophole. For example, in 2001, physicists of the U. S. National Institute of Standards and Technology and the University of Michigan53 conducted a Bell test experiment using entangled beryllium ions (9Be+). The test resulted in S = 2.25 ± 0.03, which clearly violates the S ≤ 2 limit for local hidden variables.
Another issue with the experiment we conducted is that it does not exclude the possibility that some unknown communication mechanism would be available to the photons that would allow the correlations to be higher than the classical limit of S ≤ 2. John Bell proposed that a way of closing this loophole would be to choose the settings of the polarizers only after the photons had left the source. Alain Aspect thus performed an additional experiment54 in which the polarization was changed very rapidly within the experiment, ensuring that detected photons had already left the source before the polarization state was set. Since then, ever more sophisticated experiments—including experiments by Nicolas Gisin’s group at the University of Geneva55 using detectors 18 km apart—have confirmed that there is indeed a strange “quantum connectedness” between the two particles in an EPR experiment. Somehow each “knows” what is happening with the other.
One last important thing to mention is that, although quantum physics shows that entangled particles in different places remain “connected” regardless of how much time or space separates them, this “spooky action at a distance” does not violate the Theory of Relativity, because it is impossible to use the effect to send information.
This requires a bit of explanation: the stream of counts coming out of only one of our detectors in Figure 147 will be just a random sequence, regardless of the orientations of the polarizers. That is, we cannot change around the polarizer on the other detector to send a message via entanglement. Any information encoded in the entanglement is only extractable when you look at correlations between measurements on both the entangled photons. However, to access that correlation information, you need conventional (i.e., not faster than light) communication between the detectors and the coincidence counter.
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