利用Schur-Weyl分解实现三量子比特的纠缠蒸馏
Entanglement distillation using Schur-Weyl decomposition for three qubits
摘要：
这项工作的目的是研究纠缠蒸馏发生在三量子比特系统的指数率。我们将遵循的方法来阐明纠缠浓度是基于Schur-Weyl分解和Keyl-Werner定理。为了清楚地说明这项工作的主要结果，我们将不得不介绍的概念SLOCC等价和协变代数，这将使我们能够分类状态在不同的\emph{entanglement classes}。我们的主要结果包括在一个不变的子空间中的Wedderburn分解的状态与有效的Kronecker系数$g_{αβγ}=1$的概率的渐近速率。我们还将提出一个组合公式的有效克罗内克系数的两行杨图。通过这项工作，我们希望阐明一个多体系统是如何纠缠的，以及我们可以以何种速率传递纠缠以供进一步应用。
英文摘要：
The aim of this work is to examine the exponential rates at which entanglement distillation occur in three-qubits systems. The approach we will follow to elucidate the entanglement concentration is based on the Schur-Weyl decomposition and the Keyl-Werner theorem. In order to clearly state the main results of this work we will have to introduce the notion of SLOCC equivalence and the covariant algebra which will allow us to classify states in different \emph{entanglement classes}. Our main results comprehend the asymptotic rates for the probability of being in an invariant subspace in the Wedderburn decomposition of the state with effective Kronecker coefficient $g_{αβγ}=1$. We will also present a combinatorial formula for the effective Kronecker coefficient for two-row Young diagrams. With this work we hope to shed some light in the way a multipartite system is entangled and at which rate can we convey entanglement for further applications.
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