This work provides a comprehensive approach to analyze the entanglement between subsystems generated by identical particles, based on the symmetric/exterior algebra (SEA) and microcausality. Our method amends the no-labeling approach (NLA) to quantify any type of identical particles’ entanglement, especially fermions with the parity superselection rule. We can analyze the non-local properties of identical particles’ states in a fundamentally equivalent way to those for non-identical particles, which is achieved by the factorizability of the total Hilbert space of identical particles. This formal correspondence between identical and non-identical particle systems turns out to be useful for quantifying the non-locality generated by identical particles, such as the maximal CHSH inequality violation and the GHJW theorem of identical particles.

这项工作提供了一种基于对称/外部代数（SEA）和微因果关系来分析由相同粒子生成的子系统之间的纠缠的综合方法。我们的方法对无标记方法（NLA）进行了修改，以量化任何类型的相同粒子的纠缠，尤其是具有奇偶性超选择规则的费米子。我们可以从根本上等效于分析相同粒子状态的非局部性质的方式来分析相同粒子状态的非局部性质，这是通过对相同粒子的总希尔伯特空间进行因式分解来实现的。完全相同和不同的粒子系统之间的这种形式对应关系对于量化由相同粒子生成的非局部性（例如最大CHSH不等式违规和相同粒子的GHJW定理）非常有用。