  Quantum entanglement, perhaps the most non-classical manifestation of quantum
information theory, cannot be used to transmit information between remote
parties. Yet, it can be used to reduce the amount of communication required to
process a variety of distributed computational tasks. We speak of
pseudo-telepathy when quantum entanglement serves to eliminate the classical
need to communicate. In earlier examples of pseudo-telepathy, classical
protocols could succeed with high probability unless the inputs were very
large. Here we present a simple multi-party distributed problem for which the
inputs and outputs consist of a single bit per player, and we present a perfect
quantum protocol for it. We prove that no classical protocol can succeed with a
probability that differs from 1/2 by more than a fraction that is exponentially
small in the number of players. This could be used to circumvent the detection
loophole in experimental tests of nonlocality.
