  The counterintuitive effect of non-unique ordering of two-qubit states with
quantum entanglement measures was discovered over ten years ago. More
precisely, it was shown by Monte Carlo simulations that there exist states for
which the entanglement of formation and the negativity do not impose the same
ordering of states, i.e. $E_{F}(\rho_{AB}) \leq (\geq)
E_{F}(\rho_{AB}^{\prime})$ is not equivalent to $N(\rho_{AB}) \leq (\geq)
N(\rho_{AB}^{\prime})$. Recently, it was discovered that quantum discord and
the geometric quantum discord do not necessarily imply the same ordering of
two-qubit $X$-states, which means that the lack of the unique ordering of
states with quantum entanglement measures goes beyond entanglement. Inspired by
this observation, we study the problem of the states ordering with quantum
discords, considering two-qubit Bell-diagonal states for analytical simplicity.
In particular, we identify some classes of states for which the states ordering
with quantum discords is preserved as long as the states belong to the same
class and give a few illustrative examples.
