Figure 1. Illustration of the scenario.

A measurement is carried out on a particle, depicted as a photon measured using an arrangement comprising a polarizing beam splitter and two detectors. The measurement choice (the angle of the polarizing beam splitter) is denoted A and the outcome, X, is assigned −1 or 1 depending on which detector fires. On the right, we represent the additional information that may be provided by an extended theory, Ξ, shown here taking the form of either (a) hidden variables, that is, a classical list assigning outcomes, or (b) a more general (for example, quantum) system.