近日，清华大学尤力团队研究了纯任意子态中贝尔非定域的超激活。这一研究成果于2025年12月23日发表在《物理评论A》杂志上。

标准量子信息理论建立在多方态空间具有张量积结构的基本假设之上。任意子作为容错量子计算中信息载体的候选者，由于其态空间不具备张量积结构，表现出与传统量子系统相异的独特纠缠特性。

研究组分析了任意子态中贝尔非定域性与纠缠之间的关系。具体而言，他们发现某些具有非零任意子纠缠熵的纯态本身是定域的，但在对多个副本进行联合测量时却展现出非定域性，这种现象被称为非定域性的超激活效应，以往通常仅在传统混合态中观察到。

为分析这一现象，研究组将任意子态的总纠缠分解为两个独立部分：源于张量积结构的常规纠缠，以及捕捉剩余贡献的任意子电荷纠缠。通过研究其渐近行为，他们发现随着副本数增加，常规纠缠逐渐增长并趋近于任意子纠缠熵，而任意子电荷纠缠则逐渐衰减。关键的是，他们证明对于任意子纯态，常规纠缠的存在是该态展现非定域性的充分必要条件，从而为观测到的非定域性超激活现象提供了理论解释。该研究为理解任意子系统中纠缠与非定域性的内在关联提供了新的见解。

附：英文原文

Title: Superactivation of Bell nonlocality in pure anyonic states

Author: Cheng-Qian Xu, Wenhao Ye, Li You

Issue&Volume: 2025/12/23

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.

DOI: 10.1103/bkn5-drgw

Source: https://journals.aps.org/pra/abstract/10.1103/bkn5-drgw