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Measuring multipartite entanglement through dynamic susceptibilities

Nature Physics volume 12, pages 778782 (2016) | Download Citation

Abstract

Entanglement is considered an essential resource in quantum technologies, and central to the understanding of quantum many-body physics. Developing protocols to detect and quantify the entanglement of many-particle quantum states is thus a key challenge for present experiments. Here, we show that the quantum Fisher information, a witness for genuinely multipartite entanglement, becomes measurable for thermal ensembles by means of the dynamic susceptibility—that is, with resources readily available in present cold atomic-gas and condensed-matter experiments. This establishes a connection between multipartite entanglement and many-body correlations contained in response functions, with immediate implications close to quantum phase transitions, where the quantum Fisher information becomes universal, allowing us to identify strongly entangled phase transitions with a divergent multipartite entanglement. We illustrate our framework using paradigmatic quantum Ising models, and point out potential signatures in optical-lattice experiments and strongly correlated materials.

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Acknowledgements

We thank E. Bertel, J. I. Cirac, R. Fazio, M. Mourigal, L. Pezzé and A. Smerzi for useful discussions. We acknowledge support from the EU IP SIQS, SFB FoQuS (FWF Project No. F4016-N23), the ERC synergy grant UQUAM, the Deutsche Akademie der Naturforscher Leopoldina (grant No. LPDS 2013-07 and LPDR 2015-01), Spanish Government Grant FOQUS, ERC AdG OSYRIS, EU STREP EQuaM, and EU FET Proactive QUIC. The numerical evaluation of Pfaffians uses the algorithm provided in ref. 58.

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Affiliations

  1. Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria

    • Philipp Hauke
    • , Markus Heyl
    •  & Peter Zoller
  2. Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria

    • Philipp Hauke
    • , Markus Heyl
    •  & Peter Zoller
  3. Physik Department, Technische Universität München, 85747 Garching, Germany

    • Markus Heyl
  4. ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain

    • Luca Tagliacozzo
  5. Department of Physics and Scottish Universities Physics Alliance University of Strathclyde, Glasgow G4 0NG, UK

    • Luca Tagliacozzo

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Contributions

All authors devised the project, discussed the results, and wrote the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Philipp Hauke.

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DOI

https://doi.org/10.1038/nphys3700