dorsal/arxiv
View SchemaLocalizable Entanglement
| Authors | M. Popp, F. Verstraete, M. A. Martin-Delgado, J. I. Cirac |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411123 |
| URL | https://arxiv.org/abs/quant-ph/0411123 |
| DOI | 10.1103/PhysRevA.71.042306 |
| Journal | Phys. Rev. A 71, 042306 (2005) |
Abstract
We consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins. This concept of Localizable Entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations. For both spin-1/2 and spin-1 systems we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions. We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins. The virtues of LE are illustrated for various spin models. In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed. We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length. We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel. Furthermore, we apply the numerical method to mixed states and study the entanglement as a function of temperature.
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"abstract": "We consider systems of interacting spins and study the entanglement that can\nbe localized, on average, between two separated spins by performing local\nmeasurements on the remaining spins. This concept of Localizable Entanglement\n(LE) leads naturally to notions like entanglement length and entanglement\nfluctuations. For both spin-1/2 and spin-1 systems we prove that the LE of a\npure quantum state can be lower bounded by connected correlation functions. We\nfurther propose a scheme, based on matrix-product states and the Monte Carlo\nmethod, to efficiently calculate the LE for quantum states of a large number of\nspins. The virtues of LE are illustrated for various spin models. In\nparticular, characteristic features of a quantum phase transition such as a\ndiverging entanglement length can be observed. We also give examples for pure\nquantum states exhibiting a diverging entanglement length but finite\ncorrelation length. We have numerical evidence that the ground state of the\nantiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum\nchannel. Furthermore, we apply the numerical method to mixed states and study\nthe entanglement as a function of temperature.",
"arxiv_id": "quant-ph/0411123",
"authors": [
"M. Popp",
"F. Verstraete",
"M. A. Martin-Delgado",
"J. I. Cirac"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"hep-th"
],
"doi": "10.1103/PhysRevA.71.042306",
"journal_ref": "Phys. Rev. A 71, 042306 (2005)",
"title": "Localizable Entanglement",
"url": "https://arxiv.org/abs/quant-ph/0411123"
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