All non-Gaussian states are advantageous for channel discrimination: Robustness of non-convex continuous variable quantum resources

TL;DR

This paper demonstrates that all non-Gaussian states in continuous variable quantum systems can be advantageous for channel discrimination tasks, extending the understanding of quantum resources beyond convex and finite-dimensional cases.

Contribution

It generalizes the concept of generalized robustness for arbitrary resource theories and applies it to show non-Gaussian states' advantage in channel discrimination, including non-convex sets.

Findings

All non-Gaussian states can provide an advantage in channel discrimination.

Provides exact formulas for robustness of non-Gaussianity of Fock states.

Develops practical methods to bound robustness in experiments.

Abstract

Which quantum phenomena are advantageous for information processing tasks? By classifying quantum states as resourceful versus non-resourceful, or free, the mathematical formalism of quantum resource theories helps to address such questions. For the task of discriminating channels applied to a probe state, it has been shown that under certain conditions -- namely, the set of free states being convex or finite dimensional -- every resourceful probe state can provide an advantage, quantified by a resource monotone known as generalized robustness. In this work, bypassing the limitations of previous studies, we define the generalized robustness for an arbitrary resource theory and show that it admits two operational interpretations. Firstly, it provides an upper bound on the maximal advantage in channel discrimination tasks implemented on multiple copies of the probe states. Secondly, in many physically relevant theories, it quantifies the advantage in single-copy channel discrimination tasks in a worst case scenario. We further present a general construction of multi-copy resource witnesses and provide practical methods to bound the generalized robustness in experiments. Finally, we apply our results to a key case study in continuous variable quantum information: the resource theory of non-Gaussianity. This theory is naturally defined by a set of free states (Gaussian states) that is non-convex and infinite-dimensional. Our work then shows conclusively that all non-Gaussian states can provide an advantage in some channel discrimination task, even those that are simply mixtures of Gaussian states and are typically disregarded for other quantum information tasks. To illustrate our findings, we provide exact formulas for the robustness of non-Gaussianity of Fock states, along with an analysis of the robustness for a family of non-Gaussian states within the convex hull of Gaussian states.