Figure 6: Allowed values of the decoherence quantity for measured CHSH values.
(a) shows what values of the decoherence quantity are compatible with some measured CHSH value β, assuming either quantum theory or any other probabilistic theory. The dark green region consists of all points (β, Dec(A|E)ρ) for which there exists a quantum state ρAB and two pairs (A0, A1) and (B0, B1) of observables with the according values, that is, the bound is tight. The red region shows pairs (β, Dec(A|E)ω) that cannot be realized in any non-signalling probabilistic theory. The curve between the light green area and the red area is a bound on Dec(A|E)ω which is valid for all non-signalling generalized probabilistic theories (GPTs). (b) shows a zoomed-in plot of the border line between the forbidden region and the region which is potentially allowed by GPTs. In a world constrained only by no-signalling, β=4 is possible51,52,53,54.
