Conversion of Gaussian states under incoherent Gaussian operations

The coherence resource theory needs to study the operational value and efficiency which can be broadly formulated as question: when one coherent state converted into another under incoherent operations. We answer this question completely for one-mode continuous-variable systems by characterizing conversion of Gaussian states operations in terms their first second moments. no-go theorem purification is also built. structure two-mode discussed further applied pure with standard moments are images all local linear unitary Bogoliubov As concrete applications, we obtain some peculiarities a system: (1) There does not exist maximally generate states; (2) between reversible; (3) input output equal.