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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 demonstrate a Bell state analyzer that operates directly on frequency mismatch. Based on electro-optic modulators and Fourier-transform pulse shapers, our quantum frequency processor design implements interleaved Hadamard gates in discrete frequency modes. Experimental tests on entangled-photon inputs reveal fidelities of$\sim <\#comment/>98\mathrm{\%<\#comment/>}$for discriminating between the$|{\mathrm{\Psi <\#comment/>}}^{+}⟩<\#comment/>$and$|{\mathrm{\Psi <\#comment/>}}^{-<\#comment/>}⟩<\#comment/>$frequency-bin Bell states. Our approach resolves the tension between wavelength-multiplexed state transport and high-fidelity Bell state measurements, which typically require spectral indistinguishability.