We find that the presence of strong non-Abelian symmetries can lead to highly entangled stationary states even for unital quantum channels. We derive exact expressions for the bipartite logarithmic negativity, Rényi negativities, and operator space entanglement for stationary states restricted to one symmetric subspace, with focus on the trivial subspace. We prove that these apply to open quantum evolutions whose commutants, characterizing all strongly conserved quantities, correspond to either the universal enveloping algebra of a Lie algebra or the Read-Saleur commutants. The latter provides an example of quantum fragmentation, whose dimension is exponentially large in system size. We find a general upper bound for all these quantities given by the logarithm of the dimension of the commutant on the smaller bipartition of the chain. As Abelian examples, we show that strong U(1) symmetries and classical fragmentation lead to separable stationary states in any symmetric subspace. In contrast, for non-Abelian SU(N) symmetries, both logarithmic and Rényi negativities scale logarithmically with system size. Finally, we prove that, while Rényi negativities with n>2 scale logarithmically with system size, the logarithmic negativity (as well as generalized Rényi negativities with n<2) exhibits a volume-law scaling for the Read-Saleur commutants. Our derivations rely on the commutant possessing a Hopf algebra structure in the limit of infinitely large systems and, hence, also apply to finite groups and quantum groups. Published by the American Physical Society 2025

中文翻译：

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来自强对称性的高度纠缠稳态


我们发现，即使对于幺正量子通道，强非阿贝尔对称性的存在也会导致高度纠缠的稳态。我们推导出了仅限于一个对称子空间的稳态的二分对数负性、Rényi 负性和算子空间纠缠的精确表达式，重点是琐碎的子空间。我们证明这些适用于开放量子演化，其交换子表征所有强守恒量，对应于 Lie 代数的通用包络代数或 Read-Saleur 交换子。后者提供了一个量子碎片化的例子，其维度在系统大小上呈指数级增长。我们找到所有这些量的一般上限，该上限由链的较小二分上交换子的维度的对数给出。作为阿贝尔的例子，我们表明强 U（1） 对称性和经典碎裂导致在任何对称子空间中产生可分离的稳态。相反，对于非阿贝尔 SU（N） 对称性，对数负值和 Rényi 负值都随系统大小呈对数缩放。最后，我们证明，虽然 n>2 的 Rényi 负性随系统大小呈对数刻度，但对数负性（以及 n<2 的广义 Rényi 负性）表现出 Read-Saleur 换层子的体积定律刻度。我们的推导依赖于在无限大系统极限内具有 Hopf 代数结构的交换子，因此也适用于有限群和量子群。 美国物理学会 2025 年出版