Entanglement of linear cluster states in terms of averaged entropies

An entanglement measure, multiple entropy measures (MEMS) was proposed recently by using the geometric mean of partial entropies over all possible i-body combinations of the quantum system. In this work, we study the average subsystem von Neumann entropies of the linear cluster state and investigated the quantum entanglement of linear cluster states in terms of MEMS. Explicit results with specific particle numbers are calculated, and some analytical results are given for systems with arbitrary particle numbers. Compared with other example quantum states such as the GHZ states and W states, the linear cluster states are "more entangled" in terms of MEMS, namely their averaged entropies are larger than the GHZ states and W states.