Co-authors: Ludovico Lami (University of Nottingham), Bartosz Regula (University of Nottingham), Xin Wang (University of Technology Sydney), Rosanna Nichols (University of Nottingham), Andreas Winter (Universitat Autonoma de Barcelona)

We develop a general framework characterizing the structure and properties of quantum resource theories for continuous-variable Gaussian states and Gaussian operations, establishing methods for their description and quantification. We 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 when an unlimited supply of the resource state is available. This places fundamental constraints on state transformations in all such Gaussian resource theories. We discuss in particular the applications to quantum entanglement, where we extend previously known results by showing that Gaussian entanglement cannot be distilled even with Gaussian operations preserving the positivity of the partial transpose, as well as to other Gaussian resources such as steering and optical nonclassicality. A unified semidefinite programming representation of all these reso urces is provided.

Related Links
https://arxiv.org/abs/1801.05450 - ArXiv preprint