Generalized coherence vector applied to coherence transformations and quantifiers

One of the main problems in any quantum resource theory is characterization conversions between resources by means free operations theory. In this work we advance on within coherence introducing generalized vector an arbitrary state. The a probability that can be interpreted as concave roof extension pure states vector. We show it completely characterizes notions being incoherent, well maximally coherent. Moreover, using notion and majorization relation, obtain necessary condition for conversion general incoherent operations. These results generalize conditions given literature, tools lattice are useful also case. Finally, introduce family quantifiers considering symmetric functions applied to compare proposal with convex measure others literature.