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arXiv quant-ph/0207149quant-phcond-mat
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基于相干态和凸集的纠缠推广

Generalizations of entanglement based on coherent states and convex sets

H. Barnum, E. Knill, G. Ortiz, L. Viola

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37 pages
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摘要：

二体系统中的非纠缠纯态是关于局域变换群的相干态。纠缠研究的哪些方面适用于广义相干态？反过来说，从研究得很好的相干态理论中，我们能学到什么关于纠缠的知识呢？考虑到这些问题，我们将非纠缠纯态作为局部李代数上的线性泛函时的极值态。因此，一个相对化的概念的纯度出现，表明有一个密切的关系，纯度，相干性和（非）纠缠。在很大程度上，这些概念可以在更一般的凸锥状态下定义和研究。基于纠缠是相对的这一想法，我们建议在偏序李代数或凸锥族的背景下考虑这些概念，例如自然产生的多体系统。纠缠的研究包括局部操作的概念，以及为了信息论的目的，纠缠的度量和缩放系统的方法，以实现渐近发展。我们提出的方法，这些可能被推广到李代数设置，并在较小程度上凸锥设置。我们这个计划的最初动机之一是理解纠缠类概念在凝聚态物质中的作用。我们讨论了我们的工作如何提供工具来分析量子相变和凝聚态系统的其他方面的相关性。

英文摘要：

Unentangled pure states on a bipartite system are exactly the coherent states with respect to the group of local transformations. What aspects of the study of entanglement are applicable to generalized coherent states? Conversely, what can be learned about entanglement from the well-studied theory of coherent states? With these questions in mind, we characterize unentangled pure states as extremal states when considered as linear functionals on the local Lie algebra. As a result, a relativized notion of purity emerges, showing that there is a close relationship between purity, coherence and (non-)entanglement. To a large extent, these concepts can be defined and studied in the even more general setting of convex cones of states. Based on the idea that entanglement is relative, we suggest considering these notions in the context of partially ordered families of Lie algebras or convex cones, such as those that arise naturally for multipartite systems. The study of entanglement includes notions of local operations and, for information-theoretic purposes, entanglement measures and ways of scaling systems to enable asymptotic developments. We propose ways in which these may be generalized to the Lie-algebraic setting, and to a lesser extent to the convex-cones setting. One of our original motivations for this program is to understand the role of entanglement-like concepts in condensed matter. We discuss how our work provides tools for analyzing the correlations involved in quantum phase transitions and other aspects of condensed-matter systems.

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