Encoding qubits into the spatial distribution of single photons and entangled photon pairs

We discuss an approach to encoding qubits in the spatial distribution of single photons and entangled-photon pairs based on utilizing the spatial parity of the photon wave fronts. Using simple optical components, that do not require nonlinearities or moving parts, we discuss implementing rotations in the Hilbert space of spatial parity and measurement of the state of parity. Using entangled photon pairs, we use spatial parity to demonstrate quantum nonlocality by violating a Bell inequality using an EPR state. We also discuss generalizations of this scheme that may allow for a larger number of qubits to be encoded per photon.