  Orbital angular momentum entanglement is one of the most intriguing topics in
quantum physics. A broad range of research have been dedicated either to
unravel its underlying physics or to expand the entanglement dimensions and
degrees. In this paper, we present a theoretical study on the orbital angular
momentum entanglement by employing the Heisenberg uncertainty principle to
quantum position correlation within the azimuthal region. In this study, we
decompose the pump light into a set of pump cone states characterized by their
radii. The OAM entanglement can be manipulated by controlling the radius of the
pump cone state, the length of the nonlinear crystal and the OAM carried by the
pump field,which is followed by a detailed discussion. We expect that our
research will bring us a deeper understanding of the OAM entanglement, and will
do help to the high-dimensional quantum information tasks based on OAM
entanglement.

Optics;Quantum Physics