We introduce and analyse a multiple-access channel with two senders and one receiver, in the presence of i.i.d. noise coming from the environment. Partial side information about the environmental states allows the senders to modulate their signals accordingly. An adversarial jammer with its own access to information on environmental states and the modulation signals can jam a fraction of the transmissions. Our results show that for many choices of the system parameters, entanglement shared between the two senders allows them to communicate at non-zero rates with the receiver, while for the same parameters the system forbids any communication without entanglement-assistance, even if the senders have access to common randomness (local correlations). A simplified model displaying a similar behaviour but with a compound channel instead of a jammer is outlined to introduce basic aspects of the modeling. We complement these results by demonstrating that there even exist model parameters for which entanglement-assisted communication is no longer possible, but a hypothetical use of nonlocal no-signalling correlations between Alice and Bob could enable them to communicate to Charlie again.
