  Quantum communication has historically been at the forefront of advancements,
from fundamental tests of quantum physics to utilizing the quantum-mechanical
properties of physical systems for practical applications. In the field of
communication complexity, quantum communication allows the advantage of an
exponential reduction in the information transmitted over classical
communication to accomplish distributed computational tasks. However, to date,
demonstrating this advantage in a practical setting continues to be a central
challenge. Here, we report an experimental demonstration of a quantum
fingerprinting protocol that for the first time surpasses the ultimate
classical limit to transmitted information. Ultra-low noise superconducting
single-photon detectors and a stable fibre-based Sagnac interferometer are used
to implement a quantum fingerprinting system that is capable of transmitting
less information than the classical proven lower bound over 20 km standard
telecom fibre for input sizes of up to two Gbits. The results pave the way for
experimentally exploring the advanced features of quantum communication and
open a new window of opportunity for research in communication complexity and
testing the foundations of physics.
