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Phys. Rev. Lett. 95, 120405 (2005) [4 pages]

Bell Inequalities for Graph States

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Otfried Gühne1, Géza Tóth2, Philipp Hyllus3,4, and Hans J. Briegel1,5
1Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, A-6020 Innsbruck, Austria
2Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany
3Institut für Theoretische Physik, Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
4Institute for Mathematical Sciences, Imperial College London, 48 Prince’s Gardens, SW7 London 2PE, United Kingdom
5Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria

Received 13 October 2004; published 14 September 2005

We investigate the nonlocal properties of graph states. To this aim, we derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, for each graph state there is an inequality maximally violated only by that state. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positivity of the partial transpose or the geometric measure of entanglement.

© 2005 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.95.120405
DOI:
10.1103/PhysRevLett.95.120405
PACS:
03.65.Ud, 02.40.−k, 03.67.Lx, 03.67.Mn