A Four-Dimensional Measurement Scheme for Single Photon Time-Polarization

We propose an experimental scheme to realize the four-dimensional projective measurements for a single photon. The photon polarization and time--energy provide the four-dimensional Hilbert space. Based on this scheme, we suggest an experiment to test the violation of Bell inequalities of
four-dimensional systems. In addition, by virtue of a maximally entangled biphoton state, we also show that it is possible to construct a quantum key distribution channel that can provide two-bit key with one pair of entangled photons.