  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 $\eta$. 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 realistic
quantum optical setup is suggested that can demonstrate a five-party quantum
protocol with higher-than-classical performance, provided $\eta>0.33$ .
