Fisher information and multiparticle entanglement

Philipp Hyllus, Wiesław Laskowski, Roland Krischek, Christian Schwemmer, Witlef Wieczorek, Harald Weinfurter, Luca Pezzé, and Augusto Smerzi
Phys. Rev. A 85, 022321 – Published 16 February 2012

Abstract

The Fisher information F gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles if the input state is separable. As a direct consequence, with such input states the shot-noise limit is the ultimate limit of precision. In this work, we go a step further by deducing bounds on F for several multiparticle entanglement classes. These bounds imply that genuine multiparticle entanglement is needed for reaching the highest sensitivities in quantum interferometry. We further compute similar bounds on the average Fisher information F¯ for collective spin operators, where the average is performed over all possible spin directions. We show that these criteria detect different sets of states and illustrate their strengths by considering several examples, also using experimental data. In particular, the criterion based on F¯ is able to detect certain bound entangled states.

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  • Received 14 October 2011

DOI:https://doi.org/10.1103/PhysRevA.85.022321

©2012 American Physical Society

Authors & Affiliations

Philipp Hyllus1,2, Wiesław Laskowski3,4,5, Roland Krischek4,5, Christian Schwemmer4,5, Witlef Wieczorek4,5,*, Harald Weinfurter4,5, Luca Pezzé6, and Augusto Smerzi1,6

  • 1INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, IT-38123 Povo, Italy
  • 2Department of Theoretical Physics, The University of the Basque Country, P.O. Box 644, ES-48080 Bilbao, Spain
  • 3Institute of Theoretical Physics and Astrophysics, University of Gdańsk, PL-80-952 Gdańsk, Poland
  • 4Fakultät für Physik, Ludwig-Maximilians Universität München, DE-80799 München, Germany
  • 5Max-Planck Institut für Quantenoptik, DE-85748 Garching, Germany
  • 6INO-CNR and LENS, Largo Fermi 6, IT-50125 Firenze, Italy

  • *Present address: Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, AT-1090 Vienna, Austria.

See Also

Multipartite entanglement and high-precision metrology

Géza Tóth
Phys. Rev. A 85, 022322 (2012)

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Vol. 85, Iss. 2 — February 2012

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