Bell Correlations at Ising Quantum Critical Points

Angelo Piga, Albert Aloy, Maciej Lewenstein, and Irénée Frérot
Phys. Rev. Lett. 123, 170604 – Published 23 October 2019

Abstract

When a collection of distant observers share an entangled quantum state, the statistical correlations among their measurements may violate a many-body Bell inequality, demonstrating a nonlocal behavior. Focusing on the Ising model in a transverse field with power-law (1/rα) ferromagnetic interactions, we show that a permutationally invariant Bell inequality based on two-body correlations is violated in the vicinity of the quantum-critical point. This observation, obtained via analytical spin-wave calculations and numerical density-matrix renormalization group computations, is traced back to the squeezing of collective-spin fluctuations generated by quantum-critical correlations. We observe a maximal violation for infinite-range interactions (α=0), namely, when interactions and correlations are themselves permutationally invariant.

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  • Received 14 July 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.170604

© 2019 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsStatistical Physics & ThermodynamicsQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Angelo Piga1,*, Albert Aloy1, Maciej Lewenstein1,2, and Irénée Frérot1,†

  • 1ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Barcelona, Spain
  • 2ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain

  • *angelo.piga@icfo.eu
  • irenee.frerot@icfo.eu

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Issue

Vol. 123, Iss. 17 — 25 October 2019

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