论文标题
用Hardy的非局部性测试多部分纠缠的结构
Testing the Structure of Multipartite Entanglement with Hardy's Nonlocality
论文作者
论文摘要
多部分量子状态可能表现出不同类型的量子纠缠，因为它们不能仅通过局部量子操作将它们相互转换，并且完全理解不同类型的多部分纠缠的数学结构是一项非常具有挑战性的任务。在本文中，从Hardy的非局部性的角度来看，我们比较了W和GHz状态，并显示了它们之间的几种至关重要的不同行为。特别是，通过为HARDY的W个状态的非局部性问题开发几何模型，我们为其最大违规概率而得出了上限，事实证明，该模型严格小于GHz状态的相应概率。这为我们提供了这两个量子状态之间的新比较，结果也与我们对GHz状态更纠缠的直觉一致。此外，我们概括了我们的方法以获得一般$ n $ qubit W状态的渐近表征，并表明当$ n $上升时，最大违规概率衰减的速度比一般$ n $ n $ qubit GHz状态的速度呈指数速度。我们提供了一些数值模拟来验证我们的理论结果。
Multipartite quantum states may exhibit different types of quantum entanglement in that they cannot be converted into each other by local quantum operations only, and fully understanding mathematical structures of different types of multipartite entanglement is a very challenging task. In this paper, from the viewpoint of Hardy's nonlocality, we compare W and GHZ states and show a couple of crucial different behaviors between them. Particularly, by developing a geometric model for the Hardy's nonlocality problem of W states, we derive an upper bound for its maximal violation probability, which turns out to be strictly smaller than the corresponding probability of GHZ state. This gives us a new comparison between these two quantum states, and the result is also consistent with our intuition that GHZ states is more entangled. Furthermore, we generalize our approach to obtain an asymptotic characterization for general $N$-qubit W states, revealing that when $N$ goes up, the speed that the maximum violation probabilities decay is exponentially slower than that of general $N$-qubit GHZ states. We provide some numerical simulations to verify our theoretical results.
