2005/10/31 by Geza Toth, G. Tóth, Otfried Gühne +2 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Bell state #Bell test experiments #Bell's theorem #CHSH inequality #Combinatorics #Discrete mathematics #Graph #Hidden variable theory #Inequality #Local hidden variable theory #Mathematical analysis #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Quantum nonlocality #Qubit #quant-ph
paper · pdf · doi:10.1103/physreva.73.022303
published as Phys. Rev. A 73, 022303 (2006) · 8 pages including 2 figures, revtex4; minor changes
openalex publication_date 2006/02/02 · arxiv created 2006/04/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present Bell inequalities for graph states with a high violation of local realism. In particular, we show that there is a basic Bell inequality for every nontrivial graph state which is violated by the state at least by a factor of 2. This inequality needs the measurement of, at most, two operators for each qubit and involves only some of the qubits. We also show that for some families of graph states composite Bell inequalities can be constructed such that the violation of local realism increases exponentially with the number of qubits. We prove that some of our inequalities are facets of the convex polytope containing the many-body correlations consistent with local hidden variable models. Our Bell inequalities are built from stabilizing operators of graph states.