Simulation of partial entanglement with one cbit and one M-box
  We present a protocol to simulate the correlations implied by nonmaximally entangled two qubit states. We extend this protocol to simulate the non-local part of these correlations. These protocols use single cbit communication and a single use of Millionaire box (M-box). To the best of our knowledge, these resources are weaker than those used in previous protocols using classical communication. 
Ali Ahanj and Pramod S. Joag