  We consider single photon realization of generalized N-qubit perfect W-states
which are suitable for perfect teleportation and superdense coding. We propose
schemes to generate generalized N-mode single photon perfect W-states and
derive entanglement conditions which for single photon states require finding
fidelity with generalized N-mode single photon perfect W-states and hence more
suitable to detect the genuine entanglement of generalized perfect W-states.
Based on the evolution of single photon wavefunction in scalable integrated
photonic lattices, we present schemes for the preparation of generalized N-mode
single photon perfect W-states at desired propagation distance. The integrated
waveguide structures can precisely be fabricated, offer low photon propagation
losses and can be integrated on a chip. We consider both planar and ring type
waveguide structures for state generation. 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
eigendecomposition of su(2) algebra operators reduces the generalized
entanglement condition to a simplified single photon separability condition. In
order to verify the entanglement of given genuinely entangled N-mode single
photon state using this condition one has to find the difference between the
state fidelities with suitably chosen pair of orthonormal generalized N-mode
single photon perfect W-states. Finally, we propose an experimental scheme to
verify the entanglement using the proposed conditions...
