Channel Nonlocality under Decoherence

We quantify in a unified approach the nonlocal resources of bipartite quantum channels and identify their component resisting the effects of dephasing noise. Despite its classical nature, we demonstrate that the latter plays a relevant role in performing quantum protocols, such as state transformations and quantum coding for noisy communication. When comparing different resource types, we show that simulating certain stochastic processes with quantum channels has a communication advantage with respect to their classical simulation, even when dephasing noise occurs. This approach also allows us to lower bound the amount of shared entanglement and communication needed to simulate bipartite quantum channels and to inner approximate the set of n-round local operations, assisted with classical communication.