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Abstract Owing in large part to the advent of integrated biphoton frequency combs, 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 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 solution that employs a pulse shaper and electro-optic phase modulator to perform random operations instead of mixing in a prescribed manner. We successfully verify the entanglement and reconstruct the full density matrix of biphoton frequency combs generated from an on-chip Si₃N₄microring resonator in up to an 8 × 8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. More generally, our employed Bayesian statistical model can be tailored to a variety of quantum systems with restricted measurement capabilities, forming an opportunistic tomographic framework that utilizes all available data in an optimal way. 

We showcase a fully on-chip CMOS-fabricated silicon photonic integrated circuit employing a bidirectionally pumped microring and polarization splitter-rotators tailored for the generation of broadband (>9 THz), high-fidelity (90–98%) polarization-entangled photons. Spanning the optical C+L-band and producing over 116 frequency-bin pairs on a 38.4-GHz-spaced grid, this source is ideal for flex-grid wavelength-multiplexed entanglement distribution in multiuser networks. 

We demonstrate a silicon photonic integrated circuit fabricated through the CMOS manufacturing process, which features a bidirectionally pumped microring to achieve over 116 high-fidelity polarization entangled channels covering the entire optical C+L-band for flex-grid entanglement distribution. 

We report on the manipulation of the time-resolved biphoton correlation function using a sub-GHz resolution silicon nitride microresonator-based spectral shaper capa-ble of programmable amplitude and phase modulation. 

We report a scheme for programming microresonator-based spectral pulse shapers and demonstrate it with a six-channel, sub-GHz linewidth, silicon photonic spectral shaper to generate arbitrary waveforms from optical lines of a 3 GHz electro-optic comb.