  In this paper, we investigate the communication cost of reproducing
Einstein-Podolsky-Rosen (EPR) steering correlations arising from bipartite
quantum systems. We characterize the set of bipartite quantum states which
admits a local hidden state model augmented with $c$ bits of classical
communication from an untrusted party (Alice) to a trusted party (Bob). In case
of one bit of information ($c=1$), we show that this set has a nontrivial
intersection with the sets admitting a local hidden state and a local hidden
variables model for projective measurements. On the other hand, we find that an
infinite amount of classical communication is required from an untrusted Alice
to a trusted Bob to simulate the EPR steering correlations produced by a
two-qubit maximally entangled state. It is conjectured that a state-of-the-art
quantum experiment would be able to falsify two bits of communication this way.
