A 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.