A brief note on the Scott measure as a multipartite entanglement criterion

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 (2015 Int. J. Quantum Inform. 13 1550 047) have calculated the entanglement quantity of a two-dimensional five-site spin system by means of the Scott measure. Their calculation presented $Q_2>Q_3$. In this note, we would like to point out that in a five-qudit system, Q ₂ does not provide a stronger entanglement than Q ₃, while there is a simple relation between them. (letter)