2008/02/29 by Itamar Pitowsky · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Bell test experiments #Binary number #CHSH inequality #Combinatorics #Cube (algebra) #Iterated function #Mathematical analysis #Mathematics #Molecular spectroscopy and chirality #Physics #Pure mathematics #Quadric #Quantum #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #Quantum correlation #Quantum discord #Quantum dynamics #Quantum mechanics #Quantum nonlocality #quant-ph
paper · pdf · doi:10.1103/physreva.77.062109
published as Physical Review A 77, 062109 (2008) · Published version, slight change in title
openalex publication_date 2008/06/18 · arxiv created 2008/06/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the set Q of quantum correlation vectors for two observers, each with two possible binary measurements. Quadric (hyperbolic) inequalities which are satisfied by every q∊Q are proved, and equality holds on a two-dimensional manifold consisting of the local boxes and all quantum correlation vectors that maximally violate the Clauser-Horne-Shimony-Holt (CHSH) inequality. The quadric inequalities are tightly related to the CHSH inequality; they are their iterated versions. Consequently, it is proved that Q is contained in a hyperbolic cube whose axes lie along the nonlocal (Popescu-Rohrlich) boxes. As an application, a tight constraint on the rate of local boxes that must be present in every quantum correlation is derived. The inequalities allow one to test the validity of quantum mechanics on the basis of data available from experiments which test the violation of the CHSH inequality. It is noted how these results can be generalized to the case of n sites, each with two possible binary measurements.