  Wiesner's unforgeable quantum money scheme is widely celebrated as the first
quantum information application. Based on the no-cloning property of quantum
mechanics, this scheme allows for the creation of credit cards used in
authenticated transactions offering security guarantees impossible to achieve
by classical means. However, despite its central role in quantum cryptography,
its experimental implementation has remained elusive because of the lack of
quantum memories and of practical verification techniques. Here, we
experimentally implement a quantum money protocol relying on classical
verification that rigorously satisfies the security condition for
unforgeability. Our system exploits polarization encoding of weak coherent
states of light and operates under conditions that ensure compatibility with
state-of-the-art quantum memories. We derive working regimes for our system
using a security analysis taking into account all practical imperfections. Our
results constitute a major step towards a real-world realization of this
milestone protocol.
