  Quantum communication complexity studies the efficiency of information
communication (that is, the minimum amount of communication required to achieve
a certain task) using quantum states. One representative example is quantum
fingerprinting, in which the simultaneous message passing model is considered
and the minimum amount of communication could be exponentially smaller than the
classical fingerprinting protocol. Experimental demonstrations based on a
practical quantum fingerprinting protocol where coherent states are used to
construct the fingerprints, have successfully shown the superiority of quantum
fingerprinting. However, as a consequence of using coherent states, the
communication time in this coherent quantum fingerprinting (CQF) protocol is
increased. Moreover, the minimum amount of information communicated in these
experimental demonstrations is largely limited by the dark counts of the single
photon detectors. Here, we propose to enhance the performance of the existing
CQF protocol through applying wavelength division multiplexing (WDM) and
simultaneous detection of multiple wavelength channels. We show that the new
WDM-CQF protocol can potentially reduce the communication time significantly.
More importantly, with the same experimental parameters, the amount of
communication is much reduced in the new scheme compared with the original CQF
protocol. The more wavelength channels are used, the less communication is
required by WDM-CQF protocol. We also perform a proof-of-concept experimental
demonstration of the new WDM-CQF protocol with 6 wavelength channels. The
experimental results further validate that the new scheme with WDM not only
beats the classical protocol, but also reduces the amount of communication
required by the original CQF protocol by more than half.
