Simulating equatorial measurements on GHZ states with finite expected communication cost

The communication cost of simulating probability distributions obtained by measuring quantum states is a natural way to quantify quantum non-locality. While much is known in the case of bipartite entanglement, little has been done in the multipartite setting. In this paper, we focus on the GHZ state. Specifically, equatorial measurements lead to correlations similar to the ones obtained with Bell states. We give a protocol to simulate these measurements on the n-partite GHZ state using O(n^2) bits of communication on average.