Maximally coherent states and coherence-preserving operations

Understand

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.