A feasible quantum communication complexity protocol

I show that a simple multi-party communication task can be performed more efficiently with quantum communication than with classical communication, even with low detection efficiency η. The task is a communication complexity problem in which distant parties need to compute a function of the distributed inputs, while minimizing the amount of communication between them. A quantum optical setup is suggested that can demonstrate a 5-party quantum protocol with higher-than-classical performance whenever η > 0.25 . In theory, quantum communication is better than classical communication. Experimentalists, on the other hand, know that even the simplest quantum communication protocols involve inefficiencies in state preparation, manipulation and measurement. It is, therefore, important to study sufficient experimental conditions for unambiguous demonstration of the advantages of quantum communication. Some tasks are only possible with quantum communication, such as unconditionally secure cryptographic key distribution [1, 2, 3]. Many authors have analyzed the experimental requirements for the security of these protocols [4, 5, 6]. For other tasks quantum communication offers an improvement of efficiency, and such is the case of.communication complexity problems [7, 8], one of which will be analyzed in this letter. In these problems many distant parties need to compute a function of the distributed inputs, while trying to minimize the amount of communication between them. This abstract problem has numerous practical applications, for example in computer networks, VLSI circuits and data structures (see [8] for a survey of the field). Quantum mechanics can enhance the performance of communication complexity protocols in two different ways [9]. The first approach is the entanglementbased model of communication complexity [10, 11, 12, 13], where in addition to the classical communication we allow the parties to do measurements on previously shared multi-party entangled states. Experimental requirements for some protocols of this kind have been studied in [14, 15], and it turns out that the high detection efficiency needed could be achieved in ion trap experiments [16].