Multi-setting Greenberger-Horne-Zeilinger theorem
arXiv:1303.7222 · doi:10.1103/PhysRevA.89.024103
Abstract
We 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.
5 pages, journal version
References in corpus (6)
- Device-independent security of quantum cryptography against collective attacks
- Greenberger-Horne-Zeilinger paradoxes from qudit graph states
- Greenberger-Horne-Zeilinger Nonlocality in Arbitrary Even Dimensions
- Rotational covariance and GHZ contradictions for three or more particles of any dimension
- Bell inequalities for three systems and arbitrarily many measurement outcomes
- Greenberger-Horne-Zeilinger theorem for N qudits
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