dorsal/arxiv
View SchemaGeneralizations of entanglement based on coherent states and convex sets
| Authors | H. Barnum, E. Knill, G. Ortiz, L. Viola |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0207149 |
| URL | https://arxiv.org/abs/quant-ph/0207149 |
| DOI | 10.1103/PhysRevA.68.032308 |
Abstract
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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"abstract": "Unentangled pure states on a bipartite system are exactly the coherent states\nwith respect to the group of local transformations. What aspects of the study\nof entanglement are applicable to generalized coherent states? Conversely, what\ncan be learned about entanglement from the well-studied theory of coherent\nstates? With these questions in mind, we characterize unentangled pure states\nas extremal states when considered as linear functionals on the local Lie\nalgebra. As a result, a relativized notion of purity emerges, showing that\nthere is a close relationship between purity, coherence and (non-)entanglement.\nTo a large extent, these concepts can be defined and studied in the even more\ngeneral setting of convex cones of states. Based on the idea that entanglement\nis relative, we suggest considering these notions in the context of partially\nordered families of Lie algebras or convex cones, such as those that arise\nnaturally for multipartite systems. The study of entanglement includes notions\nof local operations and, for information-theoretic purposes, entanglement\nmeasures and ways of scaling systems to enable asymptotic developments. We\npropose ways in which these may be generalized to the Lie-algebraic setting,\nand to a lesser extent to the convex-cones setting. One of our original\nmotivations for this program is to understand the role of entanglement-like\nconcepts in condensed matter. We discuss how our work provides tools for\nanalyzing the correlations involved in quantum phase transitions and other\naspects of condensed-matter systems.",
"arxiv_id": "quant-ph/0207149",
"authors": [
"H. Barnum",
"E. Knill",
"G. Ortiz",
"L. Viola"
],
"categories": [
"quant-ph",
"cond-mat"
],
"doi": "10.1103/PhysRevA.68.032308",
"title": "Generalizations of entanglement based on coherent states and convex sets",
"url": "https://arxiv.org/abs/quant-ph/0207149"
},
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