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We develop a general framework cha racterizing the structure and properties of quantu m resource theories for continuous-variable Gaussi an states and Gaussian operations\, establishing m ethods for their description and quantification. W e show in particular that\, under a few intuitive and physically-motivated assumptions on the set of free states\, no Gaussian quantum resource can be distilled with free Gaussian operations\, even wh en an unlimited supply of the resource state is av ailable. This places fundamental constraints on st ate transformations in all such Gaussian resource theories. We discuss in particular the application s to quantum entanglement\, where we extend previo usly known results by showing that Gaussian entang lement cannot be distilled even with Gaussian oper ations preserving the positivity of the partial tr anspose\, as well as to other Gaussian resources s uch as steering and optical nonclassicality. A uni fied semidefinite programming representation of al l these reso urces is provided.

Rela ted Links

- https://arxiv.org/abs/1801.05450 \;- ArXi v preprint

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