Classical states versus separable states
Classical states versus separable states
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经典状态与可分离状态
DOI：
10.1103/physreva.78.024303
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发表时间：
2008-08-01
影响因子：
2.9
通讯作者：
Luo, Shunlong
中科院分区：
文献类型：
--
作者：
Li, Nan;Luo, Shunlong
如果一个二分态不受某个局部von Neumann测量的干扰，则称为经典态(就关联而言)，如果它可以表示为积积态的凸组合，则称为可分态。由于正交向量具有良好的可区分性，经典态本质上可以用一种方便的二元概率分布来识别，而且它是可分离的，但反之亦然。可分离性的概念在量子信息论中起着关键作用，因为纠缠是通过可分离性来定义的。然而，可分离性的定义是临时的和正式的。本文从测量的角度给出了经典态对可分态的一个内在刻画：可分态就是经典态在高维空间与自然分割的约化。因此，纠缠态正是那些不能用经典态的约化来表示的态。这一观察突显了经典与纠缠之间隐藏的相互排斥和互补关系。
A bipartite state is called classical (with regard to correlations) if it is left undisturbed by a certain local von Neumann measurement, and is called separable if it can be represented as a convex combination of product states. Due to the perfect distinguishability of orthogonal vectors, a classical state can essentially be identified with a convenient bivariate probability distribution, and moreover, it is separable, but not vice versa. The notion of separability plays a key role in quantum information theory because entanglement is defined via separability. However, the definition of separability is ad hoc and formal. In this paper, we present an intrinsic characterization of separable states via classical states from the measurement perspective: Separable states are precisely those states that are reductions of classical states in higher dimensions with the natural partitions. Consequently, entangled states are precisely those states that cannot be represented as such reductions of classical states. This observation highlights the hidden mutually exclusive and complementary relations between classicality and entanglement.