Generation and entanglement study of N-mode single photon perfect W-state

Abstract

We propose schemes to generate N -mode single photon perfect W-state and derive entanglement conditions to detect the entanglement of all generalized N -mode single photon perfect W-states. These states are suitable for perfect teleportation and superdense coding over other maximally entangled states belonging to W-class. Based on the evolution of single photon wave function in scalable integrated photonic lattices, we present schemes for the preparation of N -mode single photon perfect W-state at desired propagation distance. The integrated waveguide structures can precisely be fabricated and offer low photon propagation losses. We consider both planar and ring type waveguide structures for generation of the N -mode single photon perfect W-state. We derive set of generalized entanglement detection conditions using sum uncertainty relations of generalized su(2) algebra operators. We show that any given genuinely entangled N -mode single photon state is a squeezed state of a specific su(2) algebra operator and can be expressed as superposition of a pair of generalized N -mode single photon perfect W-states which are eigenstates of that specific su(2) algebra operator. We further prove that the squeezed states of an su(2) algebra operator satisfy the entanglement condition obtained using that operator and hence the usefulness of the proposed set of entanglement conditions to detect the entanglement of genuinely entangled single photon states. Finally, we propose an experimental scheme to verify the entanglement of generalized N -mode single photon perfect W-states using an integrated photonic circuit that consists of directional couplers and phase shifters and show that the same photonic circuit can also be used to generate generalized N -mode single photon perfect W-states. Our results show that optical waveguide structures are ideal platforms for generation and verification of multipartite entangled states which could find novel applications in quantum information science.