Nonlocality, closing the detection loophole, and communication complexity

It is shown that the detection loophole that arises when trying to rule out local realistic theories as alternatives for quantum mechanics can be closed if the detection efficiency η>~Cd3/42^-0.0035d where d is the dimension of the bipartite entangled system and C is a positive constant. Furthermore it is argued that such an exponential decrease of the detector efficiency required to close the detection loophole is almost optimal. This optimality argument is based on a close connection that exists between closing the detection loophole and the amount of classical communication required to simulate quantum correlations when the detectors are perfect.