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arXiv 2108.08720quant-phmath-phmath.MPmath.OC
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多体Werner态的无纠缠探测

Dimension-free entanglement detection in multipartite Werner states

Felix Huber, Igor Klep, Victor Magron, Jurij Volčič

摘要:

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,都存在一个无量纲的纠缠见证.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。第一个是使用实际的代数几何应用于正多项式在一个革兰氏矩阵的条目,并在这个意义上是完整的,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。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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