  Quantum theory is the foundation of modern physics. Some of its basic
principles, such as Born's rule, however, are based on postulates which require
experimental testing. Any deviation from Born's rule would result in
higher-order interference and can thus be tested in an experiment. Here, we
report on such a test with a quantum light source based on a color center in
hexagonal boron nitride (hBN) coupled to a microcavity. Our room temperature
photon source features a narrow linewidth, high efficiency, high purity, and
on-demand single-photon generation. With the single-photon source we can
increase the interferometric sensitivity of our three-path interferometer
compared to conventional laser-based light sources by fully suppressing the
detector nonlinearity. We thereby obtain a tight bound on the third-order
interference term of $3.96(523)\times 10^{-4}$. We also measure an interference
visibility of 98.58% for our single-photons emitted from hBN at room
temperature, which provides a promising route for using the hBN platform as
light source for phase-encoding schemes in quantum key distribution.
