几何形状和产品状态
Geometry and Product States
摘要：
由于可分状态是积状态的凸组合，因此研究了积状态流形的几何形状。Sanpera，Vidal和Tarrach先前的结果进行了扩展。此外，证明了在最大混合态处，与乘积态流形相切的集合中的态是可分的;集合法线约束了所有最大纠缠态。给出了一个典型分解。令人惊讶的结果是，对于两个粒子的情况，最接近最大纠缠态的产物态是最大混合态。提供了一种算法来找到最接近的产品状态。
英文摘要：
As separable states are a convex combination of product states, the geometry of the manifold of product states is studied. Prior results by Sanpera, Vidal and Tarrach are extended. Furthermore, it is proven that states in the set tangent to the manifold of product states, at the maximally mixed state are separable; the set normal constains, among others, all maximally entangled states. A canonical decomposition is given. A surprising result is that for the case of two particles, the closest product state to the maximally entangled state is the maximally mixed state. An algorithm is provided to find the closest product state.
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