A brief review of Scott measure as a multipartite entanglement criterion

Abstract

In recent decades, various multipartite entanglement measures have been proposed by many researchers, with different characteristics. Meanwhile, Scott studied various interesting aspects of multipartite entanglement measures and he has defined a class of related multipartite entanglement measures in an obvious manner. Recently, Jafarpour et al. (Int. J. Quantum Inform. 13, 1550047 2015) have calculated the entanglement quantity of two-dimensional 5-site spin system by means of Scott measure. As it was presented in their calculation Q_{2}>Q_{3}. In this paper, we would like to point out that in the 5-qudit system, Q_{2} does not provide a stronger entanglement than Q_{3}, while there is a simple relation between them.