Unification of quantum resources in tripartite systems

TL;DR

This paper develops a unified framework to understand and quantify the interrelations and conversions among various quantum resources like entanglement, coherence, and steering in tripartite systems, revealing intrinsic connections.

Contribution

It derives exact and tradeoff relations among different quantum resources in tripartite systems, unifying their interpretation within quantum resource theories.

Findings

Derived an exact relation between geometric measure and multipartite concurrence.

Established tradeoff relations between coherence and multipartite entanglement.

Linked steering inequality violation with coherence and entanglement.

Abstract

In quantum resource theories (QRTs), there exists evidences of intrinsic connections among different measures of quantum resources, including entanglement, coherence, quantum steering, and so on. However, building the relations among different quantum resources is a vital yet challenging task in multipartite quantum systems. Here, we focus on a unified framework of interpreting the interconversions among different quantum resources in tripartite systems. In particular, an exact relation between the generalized geometric measure and the genuinely multipartite concurrence are derived for tripartite entanglement states. Then we obtain the tradeoff relation between the first-order coherence and the genuine tripartite entanglement by the genuinely multipartite concurrence and concurrence fill. Furthermore, the tradeoff relation between the maximum steering inequality violation and concurrence fill for an arbitrary three-qubit pure state is found. In addition, we investigate the close relation between the maximum steering inequality violation and the first-order coherence. The results show that these quantum resources are intrinsic related and can be converted to each other in the framework of QRTs, although they are still regarded to be different.