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It is shown that the detection loophole which arises when trying to rule outlocal realistic theories as alternatives for quantum mechanics can be closed ifthe detection efficiency $\eta$ is larger than $\eta \geq d^{1/2} 2^{-0.0035d}$where $d$ is the dimension of the entangled system. Furthermore it is arguedthat this exponential decrease of the detector efficiency required to close thedetection loophole is almost optimal. This argument is based on a closeconnection that exists between closing the detection loophole and the amount ofclassical communication required to simulate quantum correlation when thedetectors are perfect.Comment: 4 pages Latex, minor typos correcte

Nonlocality, closing the detection loophole, and communication complexity