A Quantum Measurement Scenario which Requires Exponential Classical   Communication for Simulation
  In this paper we consider the following question: how many bits of classical communication and shared random bits are necessary to simulate a quantum protocol involving Alice and Bob where they share k entangled quantum bits and do not communicate at all. We prove that 2^k classical bits are necessary, even if the classical protocol is allowed an \epsilon chance of failure. 
Allison Coates (Computer Science Division, University of California,   Berkeley)