Bell correlations at finite temperature

Matteo Fadel; Jordi Tura

doi:10.22331/q-2018-11-19-107

Bell correlations at finite temperature

¹Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
²Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany

Published:	2018-11-19, volume 2, page 107
Eprint:	arXiv:1805.00449v2
Doi:	https://doi.org/10.22331/q-2018-11-19-107
Citation:	Quantum 2, 107 (2018).

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Abstract

We show that spin systems with infinite-range interactions can violate at thermal equilibrium a multipartite Bell inequality, up to a finite critical temperature $T_c$. Our framework can be applied to a wide class of spin systems and Bell inequalities, to study whether nonlocality occurs naturally in quantum many-body systems close to the ground state. Moreover, we also show that the low-energy spectrum of the Bell operator associated to such systems can be well approximated by the one of a quantum harmonic oscillator, and that spin-squeezed states are optimal in displaying Bell correlations for such Bell inequalities.

Popular summary

Measurements on quantum-mechanical systems can display statistics that escape our intuition, developed by our every-day interaction with a "classical" world. In 1964, John Bell developed a mathematical framework (Bell experiment) that allows to distinguish between statistics that are compatible with our intuitive view of the world (local realism) and those that go beyond, which we only know how to produce using intrinsically quantum effects (Bell correlations). Observing Bell correlations in systems that are composed of few particles is possible by performing conceptually simple, albeit technically challenging, Bell experiments. The case of multipartite systems naturally presents many more challenges, both theoretically and experimentally. Recently, however, important developments in the field allowed for the experimental detection of Bell correlations in many-body systems composed of hundreds and hundreds of thousands of atoms. Apart from these tailored experiments, where Bell correlations were prepared by artificially controlling the interactions among the atoms, we may ask whether Bell correlations can naturally occur in many-body systems. Theoretically, it has been proven that the ground state of some Hamiltonians show Bell correlations, but in practice a system can never be prepared exactly in its ground state, leaving the previous question open. Here, after showing that Bell correlations occur in the ground state of a physically relevant class of spin Hamiltonians, we show that they persist at finite temperature up to a critical value. For reasonable experimental parameters, we foresee the possibility of preparing Bell-correlated many-body spin systems by just cooling their spin degree of freedom to few pico Kelvins. As a result of our analysis, we also show that these low-energy states can be well-approximated by an important class of quantum-mechanical states, called spin-squeezed states.

► BibTeX data

@article{Fadel2018bellcorrelations,
  doi = {10.22331/q-2018-11-19-107},
  url = {https://doi.org/10.22331/q-2018-11-19-107},
  title = {Bell correlations at finite temperature},
  author = {Fadel, Matteo and Tura, Jordi},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {2},
  pages = {107},
  month = nov,
  year = {2018}
}

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[3] F. Baccari, J. Tura, M. Fadel, A. Aloy, J.-D. Bancal, N. Sangouard, M. Lewenstein, A. Acín, and R. Augusiak, "Bell correlation depth in many-body systems", Physical Review A 100 2, 022121 (2019).

[4] Carlo Marconi, Andreu Riera-Campeny, Anna Sanpera, and Albert Aloy, "Robustness of nonlocality in many-body open quantum systems", Physical Review A 105 6, L060201 (2022).

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[7] A. Niezgoda, J. Chwedeńczuk, L. Pezzé, and A. Smerzi, "Detection of Bell correlations at finite temperature from matter-wave interference fringes", Physical Review A 99 6, 062115 (2019).

[8] J. Tura, A. Aloy, F. Baccari, A. Acín, M. Lewenstein, and R. Augusiak, "Optimization of device-independent witnesses of entanglement depth from two-body correlators", Physical Review A 100 3, 032307 (2019).

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Bell correlations at finite temperature

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