Method of developing analytical multipartite delocalization measures for mixed W -like states

We present a method of developing analytical measures of k-partite delocalization in arbitrary n-body W-like states, otherwise known as mixed states in the single-excitation subspace. These measures calculate the distance of a state to its closest reference state with k-1 entanglement. We find that the reference state is determined by the purity of the state undergoing measurement. Measures with up to 6-body delocalization for a 6-body system are derived in full, while an algorithm for general k-partite measures is given.