  We formulate the Frobenius-norm-based measures for quantum coherence and
asymmetry respectively. In contrast to the resource theory of coherence and
asymmetry, we construct a natural measure of quantum coherence inspired from
optical coherence theory while the group theoretical approach is employed to
quantify the asymmetry of quantum states. Besides their simple structures and
explicit physical meanings, we observe that these quantities are intimately
related to the purity (or linear entropy) of the corresponding quantum states.
Remarkably, we demonstrate that the proposed coherence quantifier is not only a
measure of mixedness, but also an intrinsic (basis-independent) quantification
of quantum coherence contained in quantum states, which can also be viewed as a
normalized version of Brukner-Zeilinger invariant information. In our context,
the asymmetry of N-qubit quantum systems is considered under local independent
and collective SU(2) transformations. Intriguingly, it is illustrated that the
collective effect has a significant impact on the asymmetry measure, and
quantum correlation between subsystems plays a non-negligible role in this
circumstance.
