Abstract
In this work, we consider the task of faithfully simulating a quantum measurement, acting on a joint bipartite quantum state, in a distributed manner. In the distributed setup, the constituent sub-systems of the joint quantum state are measured by two agents, Alice and Bob. A third agent, Charlie receives the measurement outcomes sent by Alice and Bob. Charlie uses local and pairwise shared randomness to compute a bivariate function of the measurement outcomes. The objective of three agents is to faithfully simulate the given distributed quantum measurement acting on the given quantum state while minimizing the communication and shared randomness rates. We demonstrate a new achievable information-theoretic rate-region that exploits the bivariate function using random structured POVMs based on asymptotically good algebraic codes. The algebraic structure of these codes is matched to that of the bivariate function that models the action of Charlie. The conventional approach for this class