标题： 量子破碎混合态中的纠缠成本层次结构 显示英文标题

标题： Entanglement cost hierarchies in quantum fragmented mixed states

摘要： 强对称性在对称开放量子动力学的定态上强制产生非平凡的量子纠缠模式。 具体来说，在固定对称性子空间内，即使对于无穷温度的混合态，非交换守恒量也会导致长程量子纠缠。 利用交换子代数框架，我们证明了对于这一类态，包括精确和渐近精确纠缠成本以及挤压制备纠缠在内的混合态的各种双部分纠缠度量（这些度量通常对于一般的多体混合态难以计算）是可以计算的。 特别是，我们关注由Temperley-Lieb模型产生的强对称极大混合态，该模型具有指数数量级（相对于系统大小）的非阿贝尔交换子引起的量子希尔伯特空间碎片化。 我们发现，虽然对于等大小的双分区，对数负性和“精确”纠缠成本都与系统的体积成比例，但形成纠缠、挤压制备纠缠、纠缠成本和可提取纠缠都表现出次可扩展标度。 我们将这些纠缠度量之间的分离归因于精确和渐近精确状态制备的纠缠成本之间的参数差异，并推断这是量子希尔伯特空间碎片化特定模式的结果。 显示英文摘要

摘要： Strong symmetries enforce non-trivial quantum entanglement patterns on the stationary states of symmetric open quantum dynamics. Specifically, non-commuting conserved quantities lead to long-range quantum entanglement even for infinite temperature mixed states within fixed symmetry sectors. Leveraging the commutant algebra framework, we show that various bipartite entanglement measures for mixed states -- including exact and asymptotically-exact entanglement costs and squashed entanglement, which are generally intractable for a generic many-body mixed state -- can be computed for this class of states. In particular, we focus on strongly symmetric maximally mixed states arising from the Temperley-Lieb model, which features quantum Hilbert space fragmentation with exponentially large (in system size) non-Abelian commutants. We find that while both the logarithmic negativity and the `exact' entanglement cost for equal-size bipartitions scale with the volume of the system, the entanglement of formation, squashed entanglement, entanglement cost, and distillable entanglement exhibit subextensive scaling. We relate this separation in entanglement measures to a parametric difference between the entanglement cost of exact and asymptotically-exact state preparations, and infer this to be a consequence of a particular pattern of quantum Hilbert space fragmentation.