  Entangled qudits, the high-dimensional entangled states, play an important
role in the study of quantum information. How to prepare entangled qudits in an
efficient and easy-to-operate manner is still a challenge in quantum
technology. Here, we demonstrate a method to engineer frequency entangled
qudits in a spontaneous parametric downconversion process. The proposal employs
an angle-dependent phase-matching condition in a nonlinear crystal, which forms
a classical-quantum mapping between the spatial (pump) and spectral (biphotons)
degrees of freedom. In particular, the pump profile is separated into several
bins in the spatial domain, and thus shapes the down-converted biphotons into
discrete frequency modes in the joint spectral space. Our approach provides a
feasible and efficient method to prepare a high-dimensional frequency entangled
state. As an experimental demonstration, we generate a three-dimensional
entangled state by using a homemade variable slit mask.
