Classical simulation of traceless binary observables on any bipartite quantum state

We present a protocol to simulate the quantum correlations of an arbitrary bipartite state, when the parties perform a measurement according to two traceless binary observables. We show that ${\log }_2\left(d\right)$ bits of classical communication is enough on average, where $d$ is the dimension of both systems. To obtain this result, we use the sampling approach for simulating the quantum correlations.