Method of areas for manipulating the entanglement properties of one copy of a two-particle pure entangled state
Method of areas for manipulating the entanglement properties of one copy of a two-particle pure entangled state
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DOI：
10.1103/physreva.60.1912
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发表时间：
1999-09-01
影响因子：
2.9
通讯作者：
Hardy, L
中科院分区：
文献类型：
--
作者：
Hardy, L
我们考虑的问题是如何操纵一般的两粒子纯态的纠缠特性，共享之间的爱丽丝和鲍勃，仅使用本地操作在每一端和经典通信之间的爱丽丝和鲍勃。一种方法，在这种类型的问题被发现是相当于一个问题，涉及到某些形状的剪切和粘贴沿着与某些着色问题。我们考虑两个问题。首先，我们找到了操纵态以获得最大纠缠态的最一般的方法。在这样的操作之后，纠缠态\11）+\22]+. + \mm]的概率为p（m）。我们得到一个表达式的最佳平均纠缠。此外，Lo和Popescu（e-print quant-ph/9707038）关于这个问题的一些结果给出了简单的几何证明。其次，我们考虑如何操纵一个微粒子纠缠态[psi]到另一个[psi ']。我们使用面积法推导出尼尔森定理（它陈述了这是可能的必要和充分条件）。[S1050-2947（99）01809-0]。
We consider the problem of how to manipulate the entanglement properties of a general two-particle pure state, shared between Alice and Bob, by using only local operations at each end and classical communication between Alice and Bob. A method is developed in which this type of problem is found to be equivalent to a problem involving the cutting and pasting of certain shapes along with certain coloring problems. We consider two problems. First, we find the most general way of manipulating the state to obtain maximally entangled states. After such a manipulation, the entangled states \11)+\22]+ ... + \mm] are obtained with probability p(m). We obtain an expression for the optimal average entanglement obtainable. Also, some results of Lo and Popescu (e-print quant-ph/9707038) pertaining to this problem are given simple geometric proofs. Second, we consider how to manipulate one mio-particle entangled state \psi] to another \psi'] with certainty. We derive Nielsen's theorem (which states a necessary and sufficient condition for this to be possible) using the method of areas. [S1050-2947(99)01809-0].