论文标题
纠缠子空间和通用的地方国家歧视，并带有前共享的纠缠
Entangled subspaces and generic local state discrimination with pre-shared entanglement
论文作者
论文摘要
沃尔盖特（Walgate）和斯科特（Scott）确定了可以通过LOCC测量明确区分的通用纯量子状态的最大数量[物理学杂志A：数学和理论，41：375305，08 2008]。在这项工作中，我们在更一般的环境中确定了这个数字，在该设置中，本地各方可以以资源状态的形式访问前共享的纠缠。我们发现，对于任意的纯资源状态，此数字等于可通过SLOCC从资源状态获得的纯状态集的Krull维度。令人惊讶的是，通用资源状态使该数字最大化。 当地国家歧视与纠缠子空间的话题密切相关，我们本身就研究了。我们介绍了$ r $ entangled子空间，该子空间自然会概括以前研究的空间到更高的多部分纠缠。我们使用代数几何方法来确定$ r $ entangled子空间的最大维度，并提供此类空间的新型显式结构。我们为对称和反对称$ r $ entangled子空间获得了类似的结果，分别对应于玻璃体和费米子系统的纠缠子空间。
Walgate and Scott have determined the maximum number of generic pure quantum states that can be unambiguously discriminated by an LOCC measurement [Journal of Physics A: Mathematical and Theoretical, 41:375305, 08 2008]. In this work, we determine this number in a more general setting in which the local parties have access to pre-shared entanglement in the form of a resource state. We find that, for an arbitrary pure resource state, this number is equal to the Krull dimension of (the closure of) the set of pure states obtainable from the resource state by SLOCC. Surprisingly, a generic resource state maximizes this number. Local state discrimination is closely related to the topic of entangled subspaces, which we study in its own right. We introduce $r$-entangled subspaces, which naturally generalize previously studied spaces to higher multipartite entanglement. We use algebraic-geometric methods to determine the maximum dimension of an $r$-entangled subspace, and present novel explicit constructions of such spaces. We obtain similar results for symmetric and antisymmetric $r$-entangled subspaces, which correspond to entangled subspaces of bosonic and fermionic systems, respectively.
