Multisetting Greenberger-Horne-Zeilinger theoremMultisetting Greenberger-Horne-Zeilinger theorem Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-202014enWe present a generalized Greenberger-Horne-Zeilinger (GHZ) theorem, which involves more than two local measurement settings for some parties, and cannot be reduced to one with less settings. Our results hold for an odd number of parties. We use a set of observables, which are incompatible but share a common eigenstate, here a GHZ state. Such observables are called concurrent. The idea is illustrated with an example of a three-qutrit system and then generalized to systems of higher dimensions, and more parties. The GHZ paradoxes can lead to, e.g., secret sharing protocols.http://creativecommons.org/licenses/by/4.0/Physical Review A892 Ryu Junghee Lee Changhyoup Yin Zhi Rahaman Ramij Aggelakis Dimitrios Αγγελακης Δημητριος Lee Jinhyoung Żukowski, Marek American Physical Society Quantum physics