Berlin 2005 – scientific programme
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Q: Quantenoptik und Photonik
Q 42: Quanteninformation II
Q 42.2: Talk
Tuesday, March 8, 2005, 14:15–14:30, HU Audimax
Bell inequalities for graph states — •Otfried Gühne1, Geza Toth2, Philipp Hyllus3, and Hans J. Briegel1,4 — 1Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, A-6020 Innsbruck — 2Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching — 3Institut für Theoretische Physik, Universität Hannover, Appelstraße 2, D-30167 Hannover — 4Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck
In the last years graph states have attracted an increasing interest in the field of quantum information theory. Graph states form a family of multi-qubit states which comprises many popular states such as the GHZ states and the cluster states. They also play an important role in applications. For instance, measurement based quantum computation uses graph states as resources. From a theoretical point of view, it is remarkable that graph states allow for a simple description in terms of stabilizing operators.
In this contribution, we investigate the non-local properties of graph states. We derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. 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.