  Photons may have homogeneous polarization and may carry quantized orbital
angular momentum (OAM). Photon entanglement has been realized in various
degrees of freedom such as polarization and OAM. Using a pair of orthogonally
polarized states carrying opposite-handedness quantized OAMs could create
"quantized" vector polarization states with space-variant polarization
structures. It is thus possible to extend the polarization degree of freedom
from two dimensional space to indefinite dimensional discrete Hilbert space. We
present a class of vector-polarization entangled Bell states, which use the
spatial modes of the vector fields with space-variant polarization structure.
We propose a scheme of creating the vector-polarization entangled Bell states
using a Sagnac interferometer. We also design an analyzer for identifying the
vector-polarization entangled Bell states. Such a class of entanglement is
important for quantum information science and technology, and fundamental
issues of quantum theory, due to its advantage of the increase in information
capacity.
