Proposed experiment for the quantum "Guess my number" protocol

An experimental realization of the entanglement-assisted "Guess my number" protocol for the reduction of communication complexity, introduced by Steane and van Dam, would require producing and detecting three-qubit GHZ states with an efficiency eta > 0.70, which would require single photon detectors of efficiency sigma > 0.89. We propose a modification of the protocol which can be translated into a real experiment using present-day technology. In the proposed experiment, the quantum reduction of the multi-party communication complexity would require an efficiency eta > 0.05, achievable with detectors of sigma > 0.47, for four parties, and eta > 0.17 (sigma > 0.55) for three parties.