Bell test
As of 2015[update], all Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems behave.[3][4] In 1964, John Stewart Bell proposed his famous theorem, which states that no physical theory of hidden local variables can ever reproduce all the predictions of quantum mechanics.[citation needed] A typical experiment involves the observation of particles, often photons, in an apparatus designed to produce entangled pairs and allow for the measurement of some characteristic of each, such as their spin.To address this problem, Bell proposed a mathematical description of local realism that placed a statistical limit on the likelihood of that eventuality.All these inequalities, like the original devised by Bell, express the idea that assuming local realism places restrictions on the statistical results of experiments on sets of particles that have taken part in an interaction and then separated.[citation needed] To date, all Bell tests have supported the theory of quantum physics, and not the hypothesis of local hidden variables.These efforts to experimentally validate violations of the Bell inequalities resulted in John Clauser, Alain Aspect, and Anton Zeilinger being awarded the 2022 Nobel Prize in Physics.The settings a, a′, b and b′ are generally in practice chosen to be 0, 45°, 22.5° and 67.5° respectively — the "Bell test angles" — these being the ones for which the quantum mechanical formula gives the greatest violation of the inequality.Nevertheless, despite all the deficiencies of the actual experiments, one striking fact emerges: the results are, to a very good approximation, what quantum mechanics predicts.One of the main achievements of this new branch of physics is showing that violation of Bell's inequalities leads to the possibility of a secure information transfer, which utilizes the so-called quantum cryptography (involving entangled states of pairs of particles).Some of the best known and recent experiments include: Leonard Ralph Kasday, Jack R. Ullman and Chien-Shiung Wu carried out the first experimental Bell test, using photon pairs produced by positronium decay and analyzed by Compton scattering.The third (and most famous) was arranged such that the choice between the two settings on each side was made during the flight of the photons (as originally suggested by John Bell).[16][17] In 1998 Gregor Weihs and a team at Innsbruck, led by Anton Zeilinger, conducted an experiment that closed the "locality" loophole, improving on Aspect's of 1982.This test violated the CHSH inequality by over 30 standard deviations, the coincidence curves agreeing with those predicted by quantum theory.This led to a reanalysis of the experimental data in a way which removed the coincidence loophole, and fortunately the new analysis still showed a violation of the appropriate CHSH or CH inequality.[28] On the other hand, the Christensen et al. experiment was pulsed and measurement settings were frequently reset in a random way, though only once every 1000 particle pairs, not every time.The first published experiment by Hensen et al.[10] used a photonic link to entangle the electron spins of two nitrogen-vacancy defect centres in diamonds 1.3 kilometers apart and measured a violation of the CHSH inequality (S = 2.42 ± 0.20).Notably, the experiment by Shalm et al. also combined three types of (quasi-)random number generators to determine the measurement basis choices.One of these methods, detailed in an ancillary file, is the “'Cultural' pseudorandom source” which involved using bit strings from popular media such as the Back to the Future films, Star Trek: Beyond the Final Frontier, Monty Python and the Holy Grail, and the television shows Saved by the Bell and Dr.[38] An international collaborative scientific effort used arbitrary human choice to define measurement settings instead of using random number generators.[41] The 2019 PBS Nova episode Einstein's Quantum Riddle documents this "cosmic Bell test" measurement, with footage of the scientific team on-site at the high-altitude Teide Observatory located in the Canary Islands.[42] In 2023, an international team led by the group of Andreas Wallraff at ETH Zurich demonstrated a loophole-free violation of the CHSH inequality with superconducting circuits deterministically entangled via a cryogenic link spanning a distance of 30 meters.[43] Though the series of increasingly sophisticated Bell test experiments has convinced the physics community that local hidden-variable theories are indefensible; they can never be excluded entirely.[30][31] The remaining possible theories that obey local realism can be further restricted by testing different spatial configurations, methods to determine the measurement settings, and recording devices.This was first noted by Philip M. Pearle in 1970,[50] who devised a local hidden variable model that faked a Bell violation by letting the photon be detected only if the measurement setting was favourable.[54] Historically, only experiments with non-optical systems have been able to reach high enough efficiencies to close this loophole, such as trapped ions,[55] superconducting qubits,[56] and nitrogen-vacancy centers.More recently, however, optical setups have managed to reach sufficiently high detection efficiencies by using superconducting photodetectors,[30][31] and hybrid setups have managed to combine the high detection efficiency typical of matter systems with the ease of distributing entanglement at a distance typical of photonic systems.A local hidden variable theory could exploit the memory of past measurement settings and outcomes in order to increase the violation of a Bell inequality.
The source S produces pairs of "photons", sent in opposite directions. Each photon encounters a two-channel polariser whose orientation can be set by the experimenter. Emerging signals from each channel are detected and coincidences counted by the coincidence monitor CM.
The source S produces pairs of "photons", sent in opposite directions. Each photon encounters a single channel (e.g. "pile of plates") polariser whose orientation can be set by the experimenter. Emerging signals are detected and coincidences counted by the coincidence monitor CM.
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