Fisher information and multiparticle entanglement

Year: 2012

Authors: Hyllus P., Laskowski W., Krischek R., Schwemmer C., Wieczorek W., Weinfurter H., Pezze L., Smerzi A.

Autors Affiliation: INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, IT-38123 Povo, Italy; Department of Theoretical Physics, The University of the Basque Country, P.O. Box 644, ES-48080 Bilbao, Spain; Institute of Theoretical Physics and Astrophysics, University of Gdansk, PL-80-952 Gdansk, Poland; Fakultat fur Physik, Ludwig-Maximilians Universitat Munchen, DE-80799 Munchen, Germany; Max-Planck Institut fur Quantenoptik, DE-85748 Garching, Germany; INO-CNR and LENS, Largo Fermi 6, IT-50125 Firenze, Italy

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) over bar 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) over bar is able to detect certain bound entangled states.


Volume: 85 (2)      Pages from: 022321  to: 022321

More Information: We thank G. Toth for discussions. We acknowledge support of the EU program Q-ESSENCE (Contract No. 248095), the DFG-Cluster of Excellence MAP, and of the EU project QAP. W. L. is supported by the MNiSW Grant No. N202 208538 and by the Foundation for Polish Science (KOLUMB program). The collaboration is a part of a DAAD/MNiSWprogram. W. W. and C. S. acknowledge support by QCCC of the Elite Network of Bavaria. P. H. acknowledges financial support of the ERC Starting Grant GEDENTQOPT. L. P. acknowledges financial support by MIUR through FIRB Project No. RBFR08H058.
DOI: 10.1103/PhysRevA.85.022321

Citations: 367
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