2013/03/31 by Junghee Ryu, Changhyoup Lee, Zhi Yin +4
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Combinatorics #Computer science #Discrete mathematics #Eigenvalues and eigenvectors #Greenberger–Horne–Zeilinger state #Mathematics #Observable #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum channel #Quantum entanglement #Quantum information #Quantum mechanics #Qutrit #Set (abstract data type) #State (computer science) #Theoretical physics #Topology (electrical circuits) #quant-ph
paper · pdf · doi:10.1103/physreva.89.024103
5 pages, journal version
arxiv created 2014/02/26 · openalex publication_date 2014/02/26 · arxiv updated 2014/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.