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

TL;DR

This paper explores how entanglement and classical communication resources affect the ability of cooperating receivers to decode messages over a causal broadcast channel with state depending on a modulo sum, revealing that combined resources enable secure, non-zero rate communication.

Contribution

It introduces a new analysis of a causal broadcast channel with state dependence, comparing the effects of entanglement, classical communication, and their combination on communication capacity.

Findings

Entanglement and classical communication together enable secure, non-zero rate message decoding.

Entanglement alone does not allow positive capacity.

Classical communication alone achieves positive capacity but with quadratic complexity overhead.

Abstract

We analyse a communication scenario over a particular causal broadcast channel whose state depends on a modulo sum. The receivers of the broadcast receive channel state information and collaborate to determine the channel state as to decode their private messages. Further, the receivers of the broadcast can collude up to the minimum non-collusion condition to determine state information of the other non-colluding receivers. We analyse three resource scenarios for the receivers: receivers can share entanglement without classically communicating, can just use classical communication, or have both entanglement and classical communication. Using results from secure multi-party communication, we find that when the receivers can share entanglement and communicate classically, they can receive messages from the sender at a non-zero rate with verifiable secure collaboration. In the entanglement only case a positive capacity is not possible. In the classical communication case, a non-zero rate of communication is achievable but the communication complexity overhead grows quadratically in the number of receivers versus linear in the number of receivers with entanglement.