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arXiv:2506.19735 · Physical Review Research

Bipartite entanglement measures for anyonic systems

Wenhao Ye, Li You, Cheng-Qian Xu

Published Mar 13, 2026• 0 citations

Abstract

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.

DOI: 10.1103/4nd3-k6rw

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Entangled states of quantum systems can give rise to measurement correlations of separated observers that cannot be described by local hidden variable theories. Usually, it is assumed that entanglement between particles is generated due to some distance-dependent interaction. Yet anyonic particles in two dimensions have a nontrivial interaction that is purely topological in nature. In other words, it does not depend on the distance between two particles, but rather on their exchange history. The information encoded in anyons is inherently non-local even in the single subsystem level making the treatment of anyons non-conventional. We describe a protocol to reveal the non-locality of anyons in terms of correlations in the outcomes of measurements in two separated regions. This gives a clear operational measure of non-locality for anyonic states and it opens up the possibility to test Bell inequalities in quantum Hall liquids or spin lattices.

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