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We analyse a communication scenario over a particular causal broadcastchannel whose state depends on a modulo sum. The receivers of the broadcastreceive channel state information and collaborate to determine the channelstate as to decode their private messages. Further, the receivers of thebroadcast can collude up to the minimum non-collusion condition to determinestate information of the other non-colluding receivers. We analyse threeresource scenarios for the receivers: receivers can share entanglement withoutclassically communicating, can just use classical communication, or have bothentanglement and classical communication. Using results from secure multi-partycommunication, we find that when the receivers can share entanglement andcommunicate classically, they can receive messages from the sender at anon-zero rate with verifiable secure collaboration. In the entanglement onlycase a positive capacity is not possible. In the classical communication case,a non-zero rate of communication is achievable but the communication complexityoverhead grows quadratically in the number of receivers versus linear in thenumber of receivers with entanglement.

Undoing Causal Effects of a Causal Broadcast Channel with Cooperating Receivers using Entanglement Resources