  It is shown that different distinguishability measures impose different
orderings on ensembles of $N$ pure quantum states. This is demonstrated using
ensembles of equally-probable, linearly independent, symmetrical pure states,
with the maximum probabilities of correct hypothesis testing and unambiguous
state discrimination being the distinguishability measures. This finding
implies that there is no absolute scale for comparing the distinguishability of
any two ensembles of $N$ quantum states, and that distinguishability comparison
is necessarily relative to a particular discrimination strategy.
