Multiparticle entanglement
Multiparticle entanglement
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DOI：
10.1023/a:1018808108183
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发表时间：
1999-04-01
影响因子：
1.5
通讯作者：
Sudbery, A
中科院分区：
文献类型：
--
作者：
Carteret, HA;Linden, N;Sudbery, A
greenberger - horn - zeilinger态是多粒子纠缠态中最著名的例子。在这篇文章中，我们描述了一个群论框架，我们一直在发展，以理解两个或多个量子粒子在一般状态下的纠缠。就纠缠而言，如果n个自旋为1/2的粒子在局部旋转组(U（2)(n)）的同一轨道上，则它们的两个态是等价的。我们考虑了纯态和混合态，并计算了描述这种状态所需的独立参数的数量。我们描述了一个给定等价类中状态的纠缠如何用局部旋转群作用于该类中任何状态的稳定群来表征。我们还展示了如何计算纯状态和混合状态下的局部作用组下的不变量。在混合状态的情况下，我们能够显式地展示不变量集，这些不变量集允许人们确定两个一般混合状态是否等价直至局部幺正变换。
The Greenberger-Horne-Zeilinger state is the most famous example of a state with multiparticle entanglement. In this article we describe a group theoretic framework we have been developing for understanding the entanglement in general states of two or more quantum particles. As far as entanglement is concerned, two states of n spin-1/2 particles are equivalent if they are on the same orbit of the group of local rotations (U(2)(n)). We consider both pure and mixed states and calculate the number of independent parameters needed to describe such states up to this equivalence. We describe how the entanglement of states in a given equivalence class may be characterized by the stability group of the action of th group of local rotations on any of the states in the class. We also show how to calculate invariants under the group of local actions for both pure and mixed states. In the case of mixed states we are able to explicitly exhibit sets of invariants which allow one to determine whether two generic mixed states are equivalent up to local unitary transformations.