  We derive some entanglement properties of the ground states of two classes of
quantum spin chains described by the Fredkin model, for half-integer spins, and
the Motzkin model, for integer ones. Since the ground states of the two models
are known analytically, we can calculate the entanglement entropy, the
negativity and the quantum mutual information exactly. We show, in particular,
that these systems exhibit long-distance entanglement, namely two disjoint
regions of the chains remain entangled even when the separation is sent to
infinity, i.e. these systems are not affected by decoherence. This strongly
entangled behavior, occurring both for colorful versions of the models (with
spin larger than 1/2 or 1, respectively) and for colorless cases (spin 1/2 and
1), is consistent with the violation of the cluster decomposition property.
Moreover we show that this behavior involves disjoint segments located both at
the edges and in the bulk of the chains.
