Superactivation of Bell nonlocality in pure anyonic states
Phys. Rev. A 112, 062232 – Published 23 December, 2025
DOI: https://doi.org/10.1103/bkn5-drgw
Abstract
Standard quantum information theory is founded on the assumption that multiparty state space possesses a tensor-product structure. Anyons, as candidates for information carriers in fault-tolerant quantum computing, exhibit unique entanglement properties that differ from the conventional quantum systems, resulting from the absence of a tensor-product structure in their state spaces. Here we investigate the relationship between Bell nonlocality and entanglement in anyonic states. Specifically, we find that certain pure anyonic states with nonzero 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 distinct components: Conventional entanglement (CE), which arises from the tensor-product structure, and anyonic charge entanglement (ACE), which captures residual contributions. By studying their asymptotic behavior, we find that CE gradually increases and approaches AEE while ACE diminishes with the number of copies. Crucially, we show that for pure anyonic states, the presence of nonzero CE is a necessary and sufficient condition for the state to exhibit nonlocality, thereby providing a theoretical explanation for the observed superactivation of nonlocality. Our findings provide insights into the connection between entanglement and nonlocality in anyonic systems.
