Bipartite entanglement measures for anyonic systems

As promising candidates for realizing fault-tolerant quantum computing, systems composed of anyons feature nontensor product state space due to their distinctive fusion rules, resulting in entanglement properties that differ fundamentally from those of conventional quantum systems. However, a quantitative characterization of entanglement in such systems remains elusive. In this Letter, we address this issue in bipartite settings using the framework of quantum resource theory. We propose three measures that quantify total entanglement, conventional entanglement, and anyonic charge entanglement (ACE) of a bipartite anyonic state, respectively. Our central result is summarized as a theorem: Total entanglement is composed of ACE and conventional entanglement. Geometrically, ACE measures the distance between the state and its charge-decorrelated version, while conventional entanglement is the minimal distance between the latter and the set of separable states, characterizing Bell nonlocality in the conventional sense. Our result confirms the long-standing intuition that ACE stems from the reduced dimensionality of the separable state space due to superselection and fusion constraints. Furthermore, we prove that ACE is equivalent to a previously proposed probe termed the entropy of ACE, thereby providing rigorous theoretical support for the latter’s monotonicity as an entanglement measure and extending the known correspondence between the geometric and operational characterizations of bipartite correlations to anyonic systems.