Analyzing the free states of one quantum resource theory as resource states of another

TL;DR

This paper explores how free states in one quantum resource theory can become resourceful when viewed through the lens of another, revealing complex interrelations across multiple QRTs.

Contribution

It provides a comprehensive analysis of resourcefulness of free states across various quantum resource theories, combining theoretical insights with numerical studies.

Findings

Free states can be highly resourceful in other QRTs.

Cross-theory analysis reveals complex resource interrelations.

Numerical results demonstrate diverse behaviors of resource states.

Abstract

In the context of quantum resource theories (QRTs), free states are defined as those which can be obtained at no cost under a certain restricted set of conditions. However, when taking a free state from one QRT and evaluating it through the optics of another QRT, it might well turn out that the state is now extremely resourceful. Such realization has recently prompted numerous works characterizing states across several QRTs. In this work we contribute to this body of knowledge by analyzing the resourcefulness in free states for--and across witnesses of--the QRTs of multipartite entanglement, fermionic non-Gaussianity, imaginarity, realness, spin coherence, Clifford non-stabilizerness, $S_n$-equivariance and non-uniform entanglement. We provide rigorous theoretical results as well as present numerical studies that showcase the rich and complex behavior that arises in this type of cross-examination.