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arXiv 0906.0673quant-ph
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纠缠对多量子比特态几何相位的影响

Effect of entanglement on geometric phase for multi-qubit states

Mark S. Williamson, Vlatko Vedral

摘要:

当多量子比特态在局域幺正下演化时,它可以获得几何相位,这是一个依赖于状态的投影希尔伯特空间的几何结构的特征。除了局部子系统相位之外,该几何相位的校正项可以从子系统之间的相关性出现。我们发现,对于几类纠缠态,这个修正项既可以完全用纠缠来刻画,也可以完全用经典关联来刻画。属于前一类的态是W态及其混合态,而属于后一类的态是团簇态、GHZ态和两类束缚纠缠态。我们探测这些状态的结构更精细地使用本地不变量,并建议纠缠校正的原因是一个规范场一样,$SL(2,\mathbb{C})$不变量最近推出命名为扭曲。

英文摘要:

When a multi-qubit state evolves under local unitaries it may obtain a geometric phase, a feature dependent on the geometry of the state's projective Hilbert space. A correction term to this geometric phase in addition to the local subsystem phases may appear from correlations between the subsystems. We find this correction term can be characterized completely either by the entanglement or completely by the classical correlations for several classes of entangled state. States belonging to the former set are W states and their mixtures, while members of the latter set are cluster states, GHZ states and two classes of bound entangled state. We probe the structures of these states more finely using local invariants and suggest the cause of the entanglement correction is a gauge field like $SL(2,\mathbb{C})$ invariant recently introduced named twist.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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