Gaussian quantum resource theories

TL;DR

This paper introduces a unified framework for Gaussian quantum resource theories, revealing fundamental limitations on resource distillation and providing tools for their quantification in continuous variable quantum information.

Contribution

It develops a general, rigorous framework for Gaussian resource theories, establishing no-distillation results and a semidefinite programming approach for quantification.

Findings

Gaussian resources cannot be distilled with free Gaussian operations.

Gaussian entanglement cannot be distilled even with PPT-preserving Gaussian operations.

A semidefinite programming method for resource quantification is provided.

Abstract

We develop a general framework to assess capabilities and limitations of the Gaussian toolbox in continuous variable quantum information theory. Our framework allows us to characterize the structure and properties of quantum resource theories specialized to Gaussian states and Gaussian operations, establishing rigorous methods for their description and yielding a unified approach to their 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 manipulations 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 comprehensive semidefinite programming representation of all these resources is explicitly provided.