  We study the nonlocal properties of two-qubit maximally-entangled and N-qubit
Greenberger-Horne-Zeilinger states under local decoherence. We show that the
(non)resilience of entanglement under local depolarization or dephasing is not
necessarily equivalent to the (non)resilience of Bell-inequality violations.
Apart from entanglement and Bell-inequality violations, we consider also
nonlocality as quantified by the nonlocal content of correlations, and provide
several examples of anomalous behaviors, both in the bipartite and multipartite
cases. In addition, we study the practical implications of these anomalies on
the usefulness of noisy Greenberger-Horne-Zeilinger states as resources for
nonlocality-based physical protocols given by communication complexity
problems. There, we provide examples of quantum gains improving with the number
of particles that coexist with exponentially-decaying entanglement and
non-local contents.
