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We construct a method for verifying mode entanglement of N-mode W states. Theideal W state contains exactly one excitation symmetrically shared between Nmodes, but our method takes the existence of higher numbers of excitations intoaccount, as well as the vacuum state and other deviations from the ideal state.Moreover, our method distinguishes between full N-party entanglement and stateswith M-party entanglement with M<N, including mixtures of the latter. Wespecialize to the case N=4 for illustrative purposes. In the optical case,where excitations are photons, our method can be implemented using linearoptics.

Verifying multi-partite mode entanglement of W states