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 η>0.70, which would require single photon detectors of efficiency σ>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 multiparty communication complexity would require an efficiency η>0.05, achievable with detectors of σ>0.47, for four parties, and η>0.17 (σ>0.55) for three parties.