Resource theory of quantum non-Gaussianity and Wigner negativity

TL;DR

This paper establishes a resource theory for continuous-variable quantum systems, enabling quantification of non-Gaussianity and Wigner negativity, with practical implications for quantum information processing.

Contribution

It introduces a new resource theory framework that includes realistic operations and defines a computable monotone for quantifying quantum resources.

Findings

Wigner logarithmic negativity effectively quantifies quantum resources.

The theory assesses resource content of experimentally relevant states.

Optimal resource concentration protocols are identified.

Abstract

We develop a resource theory for continuous-variable systems grounded on operations routinely available within current quantum technologies. In particular, the set of free operations is convex and includes quadratic transformations and conditional coarse-grained measurements. The present theory lends itself to quantify both quantum non-Gaussianity and Wigner negativity as resources, depending on the choice of the free-state set --- i.e., the convex hull of Gaussian states or the states with positive Wigner function, respectively. After showing that the theory admits no maximally resourceful state, we define a computable resource monotone --- the Wigner logarithmic negativity. We use the latter to assess the resource content of experimentally relevant states --- e.g., photon-added, photon-subtracted, cubic-phase, and cat states --- and to find optimal working points of some resource concentration protocols. We envisage applications of this framework to sub-universal and universal quantum information processing over continuous variables.