Cost of Exactly Simulating Quantum Entanglement with Classical Communication

We investigate the amount of communication that must augment classical local hidden variable models in order to simulate the behavior of entangled quantum systems. We consider the scenario where a bipartite measurement is given from a set of possibilities and the goal is to obtain exactly the same correlations that arise when the actual quantum system is measured. We show that, in the case of a single pair of qubits in a Bell state, a constant number of bits of communication is always sufficient—regardless of the number of measurements under consideration. We also show that, in the case of a system of $n$ Bell states, a constant times $2^n$ bits of communication is necessary.