 The first challenge is posed by the fact that the set of definite-valued properties—let us call it ‘\(S\)’—may change over time. One therefore has to define a family of maps, each one being a 1–1 map from \(S_0\) at time \(t_0\) to a different \(S_t\) at time \(t\), for any time. With such a family of maps, one can effectively define conditional probabilities within a single state space, and then translate them into “transition” probabilities. For this technique to work, \(S_t\) must have the same cardinality at any time. However, in general this is not the case: for instance, in SDMI, the number of different projectors appearing in the spectral decomposition of the density matrix may vary with time.