  Entanglement measures quantify the amount of quantum entanglement that is
contained in quantum states. Typically, different entanglement measures do not
have to be partially ordered. The presence of a definite partial order between
two entanglement measures for all quantum states, however, allows for
meaningful conceptualization of sensitivity to entanglement, which will be
greater for the entanglement measure that produces the larger numerical values.
Here, we have investigated the partial order between the normalized versions of
four entanglement measures based on Schmidt decomposition of bipartite pure
quantum states, namely, concurrence, tangle, entanglement robustness and
Schmidt number. We have shown that among those four measures, the concurrence
and the Schmidt number have the highest and the lowest sensitivity to quantum
entanglement, respectively. Further, we have demonstrated how these measures
could be used to track the dynamics of quantum entanglement in a simple quantum
toy model composed of two qutrits. Lastly, we have employed state-dependent
entanglement statistics to compute measurable correlations between the outcomes
of quantum observables in agreement with the uncertainty principle. The
presented results could be helpful in quantum applications that require
monitoring of the available quantum resources for sharp identification of
temporal points of maximal entanglement or system separability.
