Coherence measures and optimal conversion for coherent states

Abstract: We discuss a general strategy to construct coherence measures. One can build an important class of coherence measures which cover the relative entropy measure for pure states, the $l_1$-norm measure for pure states and the $\alpha$-entropy measure. The optimal conversion of coherent states under incoherent operations is presented which sheds some light on the coherence of a single copy of a pure state.