  Quantum coherence as an important physical resource plays the key role in
implementing various quantum tasks, whereas quantum coherence is often
deteriorated due to the noise. In this paper, we analyse under which dynamical
conditions the $l_1$-norm or the relative entropy of coherence can remain
unchanged during the whole evolution (freezing coherence). For single qubit
systems, a nice formula is given to realize freezing coherence. Conversely, for
a $d\ (d>2)$ dimensional system, we identify universal geometric conditions of
freezing coherence. This offers an affirmative answer to the open question: how
can one determine whether a unital quantum operation can be decomposed as a
convex combination of unitary operations [M. A. Nielsen and I. L. Chuang,
Quantum Computation and Quantum Information, (Cambridge University Press,
Cambridge, 2000)]. Based on this analysis, we also give a complete
classification of coherent states from operational coherence theory. This
builds the counterpart of entanglement classification under LOCC.
