Browsing by Subject "Quantum nonlocality"
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Item Open Access Bounding the Set of Finite Dimensional Quantum Correlations(American Physical Society, 2015) Navascués, M.; Vértesi, T.We describe a simple method to derive high performance semidefinite programing relaxations for optimizations over complex and real operator algebras in finite dimensional Hilbert spaces. The method is very flexible, easy to program, and allows the user to assess the behavior of finite dimensional quantum systems in a number of interesting setups. We use this method to bound the strength of quantum nonlocality in Bell scenarios where the dimension of the parties is bounded from above. We derive new results in quantum communication complexity and prove the soundness of the prepare-and-measure dimension witnesses introduced in Gallego et al., Phys. Rev. Lett. 105, 230501 (2010). Finally, we propose a new dimension witness that can distinguish between classical, real, and complex two-level systems. © 2015 American Physical Society. © 2015 American Physical Society.Item Open Access Generic entangled states as the su(2) phase states(World Scientific Publishing, 2005) Binicioǧlu, S.; Çakir, Ö.; Klyachko, A. A.; Shumovsky, A. S.We discuss an algebraic way to construct generic entangled states of qunits based on the polar decomposition of the su(2) algebra. In particular, we show that these states can be defined as eigenstates of certain Hermitian operators.Item Open Access Topological methods for studying contextuality: N-Cycle scenarios and beyond(MDPI AG, 2023-07-27) Kharoof, Aziz; İpek, Selman; Okay, CihanSimplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize nonsignaling distributions on contextuality scenarios. This paper studies simplicial distributions on two-dimensional measurement spaces by introducing new topological methods. Two key ingredients are a geometric interpretation of Fourier–Motzkin elimination and a technique based on the collapsing of measurement spaces. Using the first one, we provide a new proof of Fine’s theorem characterizing noncontextual distributions in N-cycle scenarios. Our approach goes beyond these scenarios and can describe noncontextual distributions in scenarios obtained by gluing cycle scenarios of various sizes. The second technique is used for detecting contextual vertices and deriving new Bell inequalities. Combined with these methods, we explore a monoid structure on simplicial distributions.