Maximally coherent states and coherence-preserving operations

We investigate 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 a resource to create arbitrary quantum states of the same dimension by merely incoherent operations. We propose that only 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 that excludes invalid and inefficient coherence measures. Under this criterion, we then give a measure-independent definition of the coherence-preserving operations, which play a role in quantifying coherence similar to that played by the local unitary operations in the scenario of studying entanglement.