Quantum Resource Theories of Anyonic Entanglement

TL;DR

This paper develops a resource theory framework for quantifying different types of entanglement in anyonic systems, revealing their unique entanglement structures and providing geometric and operational insights.

Contribution

It introduces three measures for total, conventional, and anyonic charge entanglement, and demonstrates their decomposition and geometric interpretation in anyonic quantum systems.

Findings

Total entanglement decomposes into conventional and anyonic charge entanglement.

The ACE measure has a geometric interpretation and is equivalent to a previous probe.

The work broadens understanding of entanglement in non-tensor product quantum systems.

Abstract

As information carriers for fault-tolerant quantum computing, systems composed of anyons exhibit non-tensor product state spaces due to their distinctive fusion rules, leading to fundamentally different entanglement properties from conventional quantum systems. However, a quantitative characterization of entanglement for general anyonic states remains elusive. In this Letter, within the framework of resource theory, we propose three measures that quantify total entanglement, conventional entanglement, and anyonic charge entanglement (ACE), respectively. We demonstrate that total entanglement can be decomposed into conventional entanglement and ACE, revealing distinct entanglement structures in anyonic systems compared to those in conventional quantum systems. We further illustrate a geometric interpretation of our ACE measure and establish its equivalence to a previously proposed probe of ACE, extending the known equivalence between the geometric interpretation and operational significance of bipartite correlations. Our work broadens the understanding of entanglement.