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High-dimensional frequency entanglement is an enabling resource in quantum technology due to its high information capacity and error resilience.A concise yet efficient method for precisely quantifying its dimensionality remains an open challenge, owing to the difficulties for performing required superposition measurements in energy-time domains, and the complexity associated with full quantum state tomography that scales unfavorably with dimensions. With the assistance of Hong-Ou-Mandel experiment that performs a Fourier transform between the entangled photons in terms of joint spectral intensities and the quantum interference in terms of biphoton temporal coincidences, the concept of Shannon dimensionality as a fast quantifier of bipartite continuous frequency entanglement is unlocked. This quantitative technique reveals the complete distribution of frequency entanglement but without suffering from any limitation of modal capacity of the detection geometry. These results may significantly facilitate the use of quantum interference for characterizing the high-dimensional entanglement nature by avoiding some stringent conditions.

Two-photon excitation spectroscopy is a nonlinear technique that has gained rapidly in interest and significance for studying the complex energy-level structure and transition probabilities of materials. While the conventional spectroscopy based on tunable classical light has been long established, quantum light provides an alternative way towards excitation spectroscopy with potential advantages in temporal and spectral resolution, as well as reduced photon fluxes. By using a quantum Fourier transform that connects the sum-frequency intensity and N00N-state temporal interference, we present an approach for quantum interferometric two-photon excitation spectroscopy. Our proposed protocol overcomes the difficulties of engineering two-photon joint spectral intensities and fine-tuned absorption-frequency selection. These results may significantly facilitate the use of quantum interferometric spectroscopy for extracting the information about the electronic structure of the two-photon excited-state manifold of atoms or molecules without any requirement for precise and complicated scanning in the spectral domain. This may be particularly relevant for photon-sensitive biological and chemical samples.

Wave-particle duality is a counterintuitive nature of quantum physics that challenges many common-sense assumptions, and Young's double-slit interference is a prototypical example. While most quantum erasure experiments emphasized the choice of erasing or marking the which-path information of one quantum system, we use frequency entanglement to report a nonlocal temporal double-slit interferometer such that the which-time information determines the wave-like or particle-like behaviors. Since frequency-entangled photons are created simultaneously by using spontaneous parametric down conversion, the mark of temporal distinguishability is readily prepared by delaying one of the entangled photons, and its quantum eraser is implemented by using spectrally resolved detection with a tunable delayed choice. These results may provide an alternative aspect and insight into the role of the temporal degree in quantum-light complementarity and photon interference.

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