Dimension-Free Entanglement Detection in Multipartite Werner States
Dimension-Free Entanglement Detection in Multipartite Werner States
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DOI：
10.1007/s00220-022-04485-9
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发表时间：
2021-08
影响因子：
2.4
通讯作者：
Felix Huber;I. Klep;Victor Magron;Jurij Volčič
中科院分区：
文献类型：
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作者：
Felix Huber;I. Klep;Victor Magron;Jurij Volčič
维尔纳态是在酉群的对角共轭作用下不变的多体量子态。本文给出了它们的纠缠的一个完整的刻画，它与局部希尔伯特空间无关：对于每一个纠缠的Werner态，都存在一个无维纠缠见证。这种证人的建设制定为一个优化问题。为了解决这个问题，两个半定规划层次的介绍。第一个是使用真实的代数几何应用于正多项式的一个革兰氏矩阵的条目，是完整的，在这个意义上，对于每一个纠缠的维尔纳状态，它收敛到一个证人。第二个是基于非交换变量的迹多项式的正性的平方和证书，并且是涉及较小的半定约束的松弛。
Werner states are multipartite quantum states that are invariant under the diagonal conjugate action of the unitary group. This paper gives a complete characterization of their entanglement that is independent of the underlying local Hilbert space: for every entangled Werner state there exists a dimension-free entanglement witness. The construction of such a witness is formulated as an optimization problem. To solve it, two semidefinite programming hierarchies are introduced. The first one is derived using real algebraic geometry applied to positive polynomials in the entries of a Gram matrix, and is complete in the sense that for every entangled Werner state it converges to a witness. The second one is based on a sum-of-squares certificate for the positivity of trace polynomials in noncommuting variables, and is a relaxation that involves smaller semidefinite constraints.