We discuss quantum random walk of two photons using linear optical elements.
We analyze the quantum random walk using photons in a variety of quantum states
including entangled states. We find that for photons initially in separable
Fock states, the final state is entangled. For polarization entangled photons
produced by type II downconverter, we calculate the joint probability of
detecting two photons at a given site. We show the remarkable dependence of the
two photon detection probability on the quantum nature of the state. In order
to understand the quantum random walk, we present exact analytical results for
small number of steps like five. We present in details numerical results for a
number of cases and supplement the numerical results with asymptotic analytical
results
