Sensitive single-photon test of extended quantum theory with 2D hexagonal boron nitride

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.