  In this work we analyze a non-commutativity measure of quantum correlations
recently proposed by Y. Guo [Sci. Rep. 6, 25241 (2016)]. By recourse to a
systematic survey of a two-qubit system, we detected an undesirable behavior of
such a measure related to its representation-dependence. In the case of pure
states, this dependence manifests as a non-satisfactory entanglement measure
whenever a representation other than the Schmidt's is used. In order to avoid
this dependence on the basis, we argue that a minimization procedure over the
set of all possible representations of the quantum state is required. In the
case of pure states, this minimization can be analytically performed and the
optimal basis turns out to be that of Schmidt's. In addition, the resulting
measure inherits the main properties of Guo's measure and, unlike the latter,
it reduces to a legitimate entanglement measure in the case of pure states.
Some examples involving general mixed states are also analyzed considering such
a optimization. The results show that, in most cases of interest, the use of
Guo's measure can result in a overestimation of quantum correlations. However,
since Guo's measure has the advantage of being easily computable, it might be
used as a qualitative estimator of the presence of quantum correlations.
