648 Hilbert space dimensionality in a biphoton frequency comb
Qubit entanglement is a valuable resource for quantum information processing, where increasing its dimensionality provides a pathway towards higher capacity and increased error resilience in quantum communications, cluster computation and quantum phase measurements. Time-frequency entanglement, a continuous variable subspace, enables the high-dimensional encoding of multiple qubits per particle, bounded only by the spectral correlation bandwidth and readout timing jitter. Extending from a dimensionality of two in discrete polarization variables, here we demonstrate a hyperentangled, mode-locked, biphoton frequency comb with a time-frequency Hilbert space dimensionality of at least 648. Hong-Ou-Mandel revivals of the biphoton qubits are observed with 61 time-bin recurrences, biphoton joint spectral correlations over 19 frequency-bins, and an overall interference visibility of the high-dimensional qubits up to 98.4%. We describe the Schmidt mode decomposition analysis of the high-dimensional entanglement, in both time- and frequency-bin subspaces, not only verifying the entanglement dimensionality but also examining the time-frequency scaling. We observe a Bell violation of the high-dimensional qubits up to 18.5 standard deviations, with recurrent correlation-fringe Clauser-Horne-Shimony-Holt S-parameter up to 2.771. Our biphoton frequency comb serves as a platform for dense quantum information processing and high-dimensional quantum key distribution.