Faithful Simulation of Broadcast Measurements

In this paper a central server Charlie has access to a quantum system C and measures it with a POVM $\{{\mathrm{\Lambda }}_x\}$. Alice and Bob are only interested in the partial results $g_A(x)$ respectively $g_B(x)$. Alice, Bob, and Charlie share common randomness and Alice and Bob only need to faithfully simulate their measurements. The paper develops to achievable regions for the amount of communication needed to Alice and Bob.