  We consider properties of states of many qubits, which arise after sending
certain entangled states via various noisy channels (white noise, coloured
noise, local depolarization, dephasing and amplitude damping). Entanglement of
these states is studied and their ability to violate certain classes of Bell
inequalities. States which violate them allow for higher than classical
efficiency of solving related distributed computational tasks with constrained
communication. This is a direct property of such states -- not requiring their
further modification via stochastic local operations and classical
communication such as entanglement purification or distillation procedures. We
identify novel families of multi-particle states which are entangled but
nevertheless allow local realistic description of specific Bell experiments.
For some of them, the "gap" between the critical values for entanglement and
violation of Bell inequality remains finite even in the limit of infinitely
many qubits.
