Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time–frequency entanglement, encoding multiple qubits per photon is only limited by the frequency correlation bandwidth and detection timing jitter. Here, we focus on the discrete-variable time–frequency entanglement in a biphoton frequency comb (BFC), generating by filtering the signal and idler outputs with a fiber Fabry–Pérot cavity with 45.32 GHz free-spectral range (FSR) and 1.56 GHz full-width-at-half-maximum (FWHM) from a continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC’s dimensionality doubles up to 648, after combining with its post-selected polarization entanglement, indicating a potential 6.28 bits/photon classical-information capacity. The BFC exhibits recurring Hong–Ou–Mandel (HOM) dips over 61 time bins with a maximum visibility of 98.4% without correction for accidental coincidences. In a post-selected measurement, it violates the Clauser–Horne–Shimony–Holt (CHSH) inequality for polarization entanglement by up to 18.5 standard deviations with an S-parameter of up to 2.771. It has Franson interference recurrences in 16 time bins with a maximum visibility of 96.1% without correction for accidental coincidences. From the zeroth- to the third-order Franson interference, we infer an entanglement of formation (E_of) up to 1.89 ± 0.03 ebits—where 2 ebits is the maximal entanglement for a 4 × 4 dimensional biphoton—as a lower bound on the 61 time-bin BFC’s high-dimensional entanglement. To further characterize time-binned/frequency-binned BFCs we obtain Schmidt mode decompositions of BFCs generated using cavities with 45.32, 15.15, and 5.03 GHz FSRs. These decompositions confirm the time–frequency scaling from Fourier-transform duality. Moreover, we present the theory of conjugate Franson interferometry—because it is characterized by the state’s joint-temporal intensity (JTI)—which can further help to distinguish between pure-state BFC and mixed state entangled frequency pairs, although the experimental implementation is challenging and not yet available. In summary, our BFC serves as a platform for high-dimensional quantum information processing and high-dimensional quantum key distribution (QKD).

Qudit纠缠是量子信息处理必不可少的资源，因为维数的增加为量子通信和簇态量子计算中的更高容量和更高的噪声弹性提供了一条途径。在连续可变的时频纠缠中，每个光子编码多个量子位仅受频率相关带宽和检测时序抖动的限制。在这里，我们专注于双光子频率梳（BFC）中的离散变量时频纠缠，通过使用具有45.32 GHz自由光谱范围（FSR）和1.56 GHz的光纤Fabry-Pérot腔对信号和惰轮输出进行滤波来生成来自连续波（cw）泵送的II型自发参量下变频器（SPDC）的半峰全宽（FWHM）。基于纯状态的假设，我们生成了一个BFC，其时分/频分希尔伯特空间维数至少为324。在结合其后选择的偏振纠缠之后，这种BFC的尺寸增加了一倍，达到648，表明潜在的6.28位/光子经典信息容量。BFC展示了在61个时区上反复发生的Hong-Ou-Mandel（HOM）下降，最大可见度为98.4％，未对偶然的巧合进行校正。在后选测量中，它通过偏振纠缠违反了Clauser-Horne-Shimony-Holt（CHSH）不等式的偏振纠缠高达18.5个标准差，且 28位/光子经典信息容量。BFC展示了在61个时区上反复出现的Hong-Ou-Mandel（HOM）下降，最大可见度为98.4％，而没有对偶然巧合进行校正。在后选测量中，它通过偏振纠缠违反了Clauser-Horne-Shimony-Holt（CHSH）不等式的偏振纠缠高达18.5个标准差，且 28位/光子经典信息容量。BFC展示了在61个时区上反复出现的Hong-Ou-Mandel（HOM）下降，最大可见度为98.4％，而没有对偶然巧合进行校正。在后选测量中，它通过偏振纠缠违反了Clauser-Horne-Shimony-Holt（CHSH）不等式的偏振纠缠高达18.5个标准差，且S参数高达2.771。它具有16个时区的Franson干扰重复发生，最大可见度为96.1％，无需对偶然的巧合进行校正。从零阶到三阶Franson干涉，我们可以推导形成的纠缠度（E_为）高达1.89±0.03 ebits（其中2 ebits是4×4维双光子的最大纠缠），作为61个时区BFC高维纠缠的下限。为了进一步表征时分/频分BFC，我们获得了使用具有45.32、15.15和5.03 GHz FSR的空腔生成的BFC的施密特模式分解。这些分解证实了傅立叶变换对偶的时频定标。此外，我们介绍了共轭Franson干涉法的理论-因为它具有状态的联合时空强度（JTI）的特征-尽管实验方法具有挑战性，但它可以进一步帮助区分纯态BFC和混合态纠缠频率对尚不可用。总之，