Sequences of projective measurements in generalized probabilistic models

We define a simple rule that allows us to describe sequences of projective measurements for a broad class of generalized probabilistic models. This class embraces quantum mechanics and classical probability theory, but, for example, also the hypothetical Popescu-Rohrlich box. For quantum mechanics, the definition yields the established Luders rule, which is the standard rule for updating the quantum state after a measurement. For the general case, it can be seen as being the least disturbing or most coherent way of performing sequential measurements. We show, as an example, that the Spekkens toy model (Spekkens 2007 Phys. Rev. A 75 032110) provides an instance of our definition. We also demonstrate the possibility of strong postquantum correlations as well as the existence of triple-slit correlations for certain nonquantum toy models.