  High-dimensional quantum entanglement is a cornerstone for advanced
technology enabling large-scale noise-tolerant quantum systems, fault-tolerant
quantum computing, and distributed quantum networks. The recently developed
biphoton frequency comb (BFC) provides a powerful platform for high-dimensional
quantum information processing in its spectral and temporal quantum modes. Here
we propose and generate a singly-filtered high-dimensional BFC via spontaneous
parametric down-conversion by spectrally shaping only the signal photons with a
Fabry-Perot cavity. High-dimensional energy-time entanglement is verified
through Franson-interference recurrences and temporal correlation with
low-jitter detectors. Frequency- and temporal- entanglement of our
singly-filtered BFC is then quantified by Schmidt mode decomposition.
Subsequently, we distribute the high-dimensional singly-filtered BFC state over
a 10 km fiber link with a post-distribution time-bin dimension lower bounded to
be at least 168. Our demonstrations of high-dimensional entanglement and
entanglement distribution show the capability of the singly-filtered quantum
frequency comb for high-efficiency quantum information processing and
high-capacity quantum networks.
