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Localizable entanglement

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Organization
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.
Keywords
DENSITY-MATRIX RENORMALIZATION, SPIN-SPIN INTERACTIONS, QUANTUM SPIN, 1-DIMENSIONAL CHAIN, LOCAL OPERATIONS, TRANSVERSE FIELD, GROUND-STATE, HALDANE-GAP, CHANNELS, ANTIFERROMAGNETS

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Citation

Please use this url to cite or link to this publication:

MLA
Popp, M et al. “Localizable Entanglement.” PHYSICAL REVIEW A 71.4 (2005): n. pag. Print.
APA
Popp, M., Verstraete, F., Martin-Delgado, M., & Cirac, J. (2005). Localizable entanglement. PHYSICAL REVIEW A, 71(4).
Chicago author-date
Popp, M, Frank Verstraete, MA Martin-Delgado, and JI Cirac. 2005. “Localizable Entanglement.” Physical Review A 71 (4).
Chicago author-date (all authors)
Popp, M, Frank Verstraete, MA Martin-Delgado, and JI Cirac. 2005. “Localizable Entanglement.” Physical Review A 71 (4).
Vancouver
1.
Popp M, Verstraete F, Martin-Delgado M, Cirac J. Localizable entanglement. PHYSICAL REVIEW A. 2005;71(4).
IEEE
[1]
M. Popp, F. Verstraete, M. Martin-Delgado, and J. Cirac, “Localizable entanglement,” PHYSICAL REVIEW A, vol. 71, no. 4, 2005.
@article{8594023,
  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.},
  articleno    = {042306},
  author       = {Popp, M and Verstraete, Frank and Martin-Delgado, MA and Cirac, JI},
  issn         = {1050-2947},
  journal      = {PHYSICAL REVIEW A},
  keywords     = {DENSITY-MATRIX RENORMALIZATION,SPIN-SPIN INTERACTIONS,QUANTUM SPIN,1-DIMENSIONAL CHAIN,LOCAL OPERATIONS,TRANSVERSE FIELD,GROUND-STATE,HALDANE-GAP,CHANNELS,ANTIFERROMAGNETS},
  language     = {eng},
  number       = {4},
  pages        = {18},
  title        = {Localizable entanglement},
  url          = {http://dx.doi.org/10.1103/PhysRevA.71.042306},
  volume       = {71},
  year         = {2005},
}

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