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