Two-photon Hong-Ou-Mandel (HOM) interference is a fundamental quantum effect with no classical counterpart. The existing research on two-photon interference was mainly limited in one degree of freedom (DOF); hence, it is still a challenge to realize quantum interference in multiple DOFs. Here, we demonstrate HOM interference between two hyperentangled photons in two DOFs of polarization and orbital angular momentum (OAM) for all 16 hyperentangled Bell states. We observe hyperentangled two-photon interference with a bunching effect for ten symmetric states (nine boson-boson states and one fermion-fermion state) and an antibunching effect for six antisymmetric states (three boson-fermion states and three fermion-boson states). More interestingly, expanding the Hilbert space by introducing an extra DOF for two photons enables one to transfer the unmeasurable external phase in the initial DOF to a measurable internal phase in the expanded two DOFs. We directly measured the symmetric exchange phases being $0.012\pm 0.002$, $0.025\pm 0.002$, and $0.027\pm 0.002$ in radian for the three boson states in OAM and the antisymmetric exchange phase being $0.991\pi \pm 0.002$ in radian for the other fermion state, as theoretical predictions. Our Letter may not only pave the way for more wide applications of quantum interference, but also develop new technologies by expanding Hilbert space in more DOFs.

• Received 27 June 2022
• Revised 10 October 2022
• Accepted 29 November 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.263602