  We propose the notion of faithful coherent states based on the fidelity-based
coherence witness. The criterion for detecting faithful coherent states can be
restricted to a subclass of fidelity-based criterion under unitary
transformations for single and bipartite systems. We can realize these unitary
transformations by using quantum gates and circuits, and establish the
connection of faithful coherence states and coherence distillation, maximum
relative entropy of coherence.
