  Within the decoherent histories formulation of quantum mechanics, we
investigate necessary conditions for decoherence of arbitrarily long histories.
We prove that fine-grained histories of arbitrary length decohere for all
classical initial states if and only if the unitary evolution preserves
classicality of states (using a natural formal definition of classicality). We
give a counterexample showing that this equivalence does not hold for
coarse-grained histories.
