Fisher information and entanglement of non-Gaussian spin states

Year: 2014

Authors: Strobel H., Muessel W., Linnemann D., Zibold T., Hume D.B., Pezzè L., Smerzi A., Oberthaler M.K.

Autors Affiliation: Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany; QSTAR (Quantum Science and Technology in Arcetri), INO-CNR (Istituto Nazionale di Ottica-Consiglio Nazionale Delle Ricerche), LENS (European Laboratory for Nonlinear Spectroscopy), Largo Enrico Fermi 2, 50125 Firenze, Italy

Abstract: Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian statistics. Here, we report on the creation and characterization of non-Gaussian many-body entangled states. We develop a general method to extract the Fisher information, which reveals that the quantum dynamics of a classically unstable system creates quantum states that are not spin squeezed but nevertheless entangled. The extracted Fisher information quantifies metrologically useful entanglement, which we confirm by Bayesian phase estimation with sub-shot-noise sensitivity. These methods are scalable to large particle numbers and applicable directly to other quantum systems.

Journal/Review: SCIENCE

Volume: 345      Pages from: 424  to: 427

More Information: We thank J. Tomkovic, E. Nicklas, and I. Stroescu for technical help and discussions. This work was supported by the Forschergruppe FOR760, the Deutsche Forschungsgemeinschaft, the Heidelberg Center for Quantum Dynamics, and the European Commission small or medium-scale focused research project QIBEC (Quantum Interferometry with Bose-Einstein condensates, contract no. 284584). W. M. acknowledges support by the Studienstiftung des deutschen Volkes. D. B. H. acknowledges support from the Alexander von Humboldt Foundation. L. P. acknowledges financial support by Ministero dell\’Istrzione, dell\’Università e della Ricerca through Fondo per gli Investimenti della Ricerca di Base project no. RBFR08H058. QSTAR is the Max Planck Institute of Quantum Optics, LENS, Istituto Italiano di Tecnologia, Universit degli Studi di Firenze Joint Center for Quantum Science and Technology in Arcetri.
KeyWords: fisher information; entanglement; statistical distance; quantum metrology; limit, interferometer
DOI: 10.1126/science.1250147

Citations: 305
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