阿根廷科尔多瓦国立大学A. P. Majtey团队研究了三个不可区分玻色子系统的纠缠度：重温Greenberger-Horne-Zeilinger态。2025年4月8日出版的《物理评论A》杂志发表了这项成果。

虽然可区分粒子的纠缠概念已经确立，但在不可区分粒子系统中定义纠缠和非局域性仍然具有挑战性，这需要使用（反）对称化假设，并且已经提出了多种方法来解决这个问题。

在这项工作中，课题组研究了检测不可区分玻色子系统之间真正的三重纠缠的问题。真正的纠缠态是在任何二分下都不可分离的纠缠态，其中不可区分状态下的可分离性是由每个子系统中单个粒子属性的存在来定义的，而不可能知道哪个属性属于哪个子系统。

研究组使用一种算法，该算法允许其搜索这些单粒子属性，并根据其可分离性对状态进行排序。特别是，他们引入了一种性质类似于标准Greenberger-Horne-Zeilinger态的不可区分玻色子状态。

附：英文原文

Title: Degrees of entanglement in systems of three indistinguishable bosons: Revisiting the Greenberger-Horne-Zeilinger state

Author: P. Céspedes, F. H. Holik, A. P. Majtey

Issue&Volume: 2025/04/08

Abstract: While the concept of entanglement for distinguishable particles is well established, defining entanglement and nonlocality in systems of indistinguishable particles, which require the use of the (anti)symmetrization postulate, remains challenging, and multiple approaches have been proposed to address this issue. In this work we study the problem of detecting genuine tripartite entanglement among systems of indistinguishable bosons. A genuine entangled state is one that cannot be separable under any bipartition, where separability in the indistinguishable regime is defined by the existence of single-particle properties within each subsystem, without the possibility of knowing which property belongs to which subsystem. We use an algorithm that allows us to search for these single-particle properties and consequently rank states according to their degree of separability. In particular, we introduce a state of indistinguishable bosons with properties analogous to those of the standard Greenberger-Horne-Zeilinger state.

DOI: 10.1103/PhysRevA.111.042414

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.042414