An elegant design of a waveguide array consisting of (2N-1) identical single mode optical waveguides is introduced to create ‘N’ partite two photon W state that illustrates much enhanced tolerance to the fabrication conditions and experimental perturbations.
Recently, integrated optic solutions for generating single photon N-partite W states by using a one-dimensional array of N identical single-mode optical waveguides, which are coupled via nearest-neighbour interaction, have been proposed. Due to the particular design of the proposed structure, the tolerances with respect to the length of the device and the input wavelength of the single photon for the generation of the W state are very critical, thus making an experimental realization troublesome. Here, we propose an alternative design of a waveguide array consisting of (2N-1) waveguides to create a single-photon N-partite W state that exhibits much greater tolerance to the fabrication conditions as well as to the input wavelength and hence is much more realizable experimentally. The same design is also shown to lead to the generation of two-photon W-states when using the post selection technique.
Abstract W states are maximally entangled states with excellent robustness to loss. They have been studied in ion, photon and waveguide-mode bases, however the entanglement verification has remained challenging. Here, we theoretically study W-state generation by the quantum walk of a single photon through a linearly coupled waveguide array (WGA) that supports self-imaging of light. We design W states in symmetric and asymmetric arrays with even and odd number of waveguides. Bipartite entanglement is formally proven using the von Neumann entropy of the reduced density matrix. We further use the self-imaging to construct an entanglement witness based on the exclusion principle. A key to verification is the interferometer which extends the length of a W-state generator to the revival length where the photon is fully recombined into a single waveguide mode. In addition, W-state coherence is proven by numerically demonstrating the far-field interference. The sensitivities of the proposed W-state generation and verification protocols to the fabrication tolerances are numerically evaluated in glass, silicon nitride and silicon-on-insulator WGAs, indicating the feasibility of their realisation by high-precision e-beam lithography and laser writing.