Entanglement of linear cluster states in terms of averaged entropies

Ye Cao,Hui Li,Guilu Long

doi:10.1007/s11434-012-5604-2

Abstract

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.

Highlights

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
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

Summary

Entanglement of linear cluster states in terms of averaged entropies

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. 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. Average subsystem entropies, cluster states, multiple entropy measures, quantum entanglement. Realizing the lack of one-qubit reduction, Higuchi et al [51,52] proposed using the arithmetic mean of two-particle entropies as a measure of entanglement, and reported on a four-qubit entangled state:. Liu et al [53] proposed multiple averaged entropy measures based on a vector with m = [N/2] components: [S 1 , S 2 , · · · , S m ], where the S i is the geometric mean of i-body partial entropy of the system c The Author(s) 2013.

It holds a high persistency of entanglement which means that

Times Entropy