  We investigate the maximally coherent states to provide a refinement in
quantifying coherence and give a measure-independent definition of the
coherence-preserving operations. A maximally coherent state can be considered
as the resource to create arbitrary quantum states of the same dimension by
merely incoherent operations. We propose that only the maximally coherent
states should achieve the maximal value for a coherence measure and use this
condition as an additional criterion for coherence measures to obtain a
refinement in quantifying coherence which excludes the invalid and inefficient
coherence measures. Under this new criterion, we then give a
measure-independent definition of the coherence-preserving operations, which
play a similar role in quantifying coherence as that played by the local
unitary operations in the scenario of studying entanglement.
