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Measuring multipartite entanglement through dynamic susceptibilities

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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Figure 1: Measurement prescription for the quantum Fisher information (QFI), a witness for multipartite entanglement.
Figure 2: Universal scaling of the quantum Fisher information density, fQ = FQ/N, calculated for the order parameter in the quantum Ising chain.
Figure 3: Absence of features of the quantum Fisher information at thermal phase transitions, exemplified by the infinitely connected Ising model.

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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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Correspondence to Philipp Hauke.

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Hauke, P., Heyl, M., Tagliacozzo, L. et al. Measuring multipartite entanglement through dynamic susceptibilities. Nature Phys 12, 778–782 (2016). https://doi.org/10.1038/nphys3700

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