An entangled walk of photons

Matthews, Jonathan C. F., Mark G. Thompson

Krishna Thyagarajan

Juan P. Torres, Gabriel Molina‐Terriza, Lluís Torner

We address the spatial shape of entangled photon states generated in spontaneous parametric downconversion in non-collinear geometries, when the interacting waves exhibit Poynting vector walk-off. We discuss how such shape depends on the interplay between the state ellipticity caused by the non-collinear geometry, and the Poynting vector walk-off. In particular, we study the impact of the new features exhibited by walking entangled photons on the implementation of quantum protocols based on the spiral spectra of the entangled photons.

Nicolas Gisin, John Rarity, Gregor Weihs

Pradyumna K. Pathak, G. S. Agarwal

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 such as five. We present in detail numerical results for a number of cases and supplement the numerical results with asymptotic analytical results.

David S. Simon