  High-dimensional quantum entanglement is currently one of the most prolific
fields in quantum information processing due to its high information capacity
and error resilience. A versatile method for harnessing high-dimensional
entanglement has long been hailed as an absolute necessity in the exploration
of quantum science and technologies. Here we exploit Hong-Ou-Mandel
interference to manipulate discrete frequency entanglement in
arbitrary-dimensional Hilbert space. The generation and characterization of
two-, four- and six-dimensional frequency entangled qudits are theoretically
and experimentally investigated, allowing for the estimation of entanglement
dimensionality in the whole state space. Additionally, our strategy can be
generalized to engineer higher-dimensional entanglement in other photonic
degrees of freedom. Our results may provide a more comprehensive understanding
of frequency shaping and interference phenomena, and pave the way to more
complex high-dimensional quantum information processing protocols.
