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

We propose generation and entanglement detection schemes for generalized N-mode single-photon perfect W-states. These states are suitable for perfect teleportation and superdense coding. Based on the evolution of single-photon wavefunction in scalable integrated photonic lattices, we present schemes to generate these states using both planar and ring type waveguide structures. The integrated waveguide structures can be precisely fabricated, offer low photon propagation losses and can be integrated on a chip. In addition, we derive set of generalized entanglement conditions using the 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 orthonormal generalized N-mode single-photon perfect W-states which are eigenstates of that specific su(2) algebra operator. Within the single-photon subspace, the generalized entanglement condition reduces to a simplified single-photon separability condition. Detection of entanglement of single-photon states, using this single-photon separability condition, requires finding fidelity with two pairs of orthonormal generalized N-mode single-photon perfect W-states and hence more suitable for our purpose. Finally, we propose an experimental scheme to verify the entanglement using the proposed conditions. This scheme uses a photonic circuit consisting of directional couplers and phase shifters. The same photonic circuit can also be used to generate generalized N-mode single-photon perfect W-states.