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arXiv:2506.08919 · Physical Review A

Superactivation of Bell nonlocality in pure anyonic states

Cheng-Qian Xu, Wenhao Ye, Li You

Published Dec 5, 2025• 1 citation

Abstract

Standard quantum information theory is founded on the assumption that multi-party state space possesses a tensor product structure. Anyons, as quasiparticles in two-dimensional systems, exhibit unique entanglement properties that differ from the conventional quantum systems, resulting from the absence of a tensor product structure in their state spaces. This motivates us to investigate the relationship between Bell nonlocality and entanglement in anyonic states. Specifically, we find that certain pure anyonic states with non-zero anyonic entanglement entropy (AEE) are local, yet exhibit nonlocality when subjected to collective measurements on multiple copies-a phenomenon known as superactivation of nonlocality, which is typically observed in conventional mixed states. To analyze this, we decompose the total entanglement of anyonic states into two components: one from the tensor product structure and the other representing residual contributions. By studying their asymptotic behavior, we find that the former gradually increases and approaches the AEE while the latter diminishes with the number of copies. Crucially, the entanglement component associated with the tensor product structure demonstrates a significant correlation with nonlocality, which explains the observed superactivation of nonlocality. Our findings provide new insights into the connection between entanglement and nonlocality in anyonic systems.

DOI: 10.1103/bkn5-drgw

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Quantum correlations in the form of entanglement, quantum steering or Bell nonlocality are resources for various information-processing tasks, but their detailed quantification and characterization remains complicated. One counter-intuitive effect is the phenomenon of superactivation, meaning that two copies of a quantum state may exhibit forms of correlations which are absent on the single-copy level. We develop a systematic approach towards a full understanding of this phenomenon using the paradigm of genuine multipartite entanglement. We introduce systematic methods for studying superactivation of entanglement based on symmetries and generalized notions of multipartite distillability. With this, we present novel criteria for superactivation as well as a quantitative theory of it. Moreover, we present evidence for incompressible entanglement on multi-copy systems, which cannot be reduced to the single-copy level.

Nonlocality, as an essential, subtle and intriguing aspect of nature, has many different facets and manifestations. In quantum information theory, nonlocality is usually defined, characterized and quantified in the framework of entanglement and violation of certain Bell inequalities. An exciting phenomenon concerning entanglement-related nonlocality is the superactivation, symbolized as “0 + 0 > 0”, which means that two systems, while do not possess nonlocality individually by themselves, may exhibit nonlocality when combined together in an independent fashion. In this work, we explore nonlocality from the measurement perspective and reveal the superactivation of measurement-induced nonlocality (MIN): When two bipartite states with vanishing MIN are combined together, the tensorizing state may possess non-zero MIN. Implications and applications are discussed.

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Bell’s nonlocality—correlations between two distant, entangled particles that cannot be explained by physical theories based on local causality—remains one of the most celebrated results of quantum foundations. However, these nonlocal correlations eventually disappear under the presence of noise. In this experimental work, we show that nonlocality, inaccessible for noisy states in the two-party scenario, can be activated in a three-node photonic network structure with a single copy of the state. Our results open up new possibilities for network-based quantum information processing applications, central for the development of a future quantum internet.