David Kaiser in Scientific American:

Physicists had long known that the two flavors of polarization—plane or circular—were intimately related. Plane-polarized light could be used to create circularly polarized light, and vice versa. For example, a beam of

H-polarized light consisted of equal partsR– andL-polarized light, in a particular combination, just as a beam ofR-polarized light could be broken down into equal partsHandV. Likewise for individual photons: a photon in stateR, for example, could be represented as a special combination of statesHandV. If one prepared a photon in stateRbut chose to measure plane rather than circular polarization, one would have an equal probability of findingHorV: a single-particle version of Schrödinger’s cat.In Herbert's imagined set-up, one physicist, Alice (“Detector A” in the illustration), could choose to measure either plane or circular polarization of the photon headed her way [1]. If she chose to measure plane polarization, she would measure

HandVoutcomes with equal probability. If she chose to measure circular polarization, she would findRandLoutcomes with equal probability.In addition, Alice knows that because of the nature of the source of photons, each photon she measures has an entangled twin moving toward her partner, Bob. Quantum entanglement means that the two photons behave like two sides of a coin: if one is measured to be in state

R, then the other must be in stateL; or if one is measured in stateH, the other must be in stateV. The kicker, according to Bell's theorem, is that Alice's choice of which type of polarization to measure (plane or circular) should instantly affect the other photon, streaming toward Bob [2]. If she chose to measure plane polarization and happened to get the resultH, then the entangled photon heading toward Bob would enter the stateVinstantaneously. If she had chosen instead to measure circular polarization and found the resultR, then the entangled photon instantly would have entered the stateL.Next came Herbert's special twist.