  Quantum self-testing is a device-independent way to certify quantum states
and measurements using only the input-output statistics, with minimal
assumptions about the quantum devices. Because of the high demand on tolerable
noise, however, experimental self-testing was limited to two-photon systems.
Here, we demonstrate the first robust self-testing for multi-photon genuinely
entangled quantum states. We prepare two examples of four-photon graph states,
the Greenberger-Horne-Zeilinger (GHZ) states with a fidelity of 0.957(2) and
the linear cluster states with a fidelity of 0.945(2). Based on the observed
input-output statistics, we certify the genuine four-photon entanglement and
further estimate their qualities with respect to realistic noise in a
device-independent manner.
