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Full quantum state tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements


 Owing in large part to the advent of integrated biphoton frequency combs (BFCs), recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography (QST) of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a novel solution that employs a pulse shaper and electro-optic phase modulator (EOM) to perform random operations instead of mixing in a prescribed manner. Incorporating state-of-the-art Bayesian statistical method, we successfully verify the entanglement and reconstruct the full density matrix of BFCs generated from an on-chip Si3N4 microring resonator (MRR) in up to an 8×8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. Overall, our method furnishes an experimentally powerful approach for frequency-bin tomography with readily implementable operations.