title: Bounding the Set of Finite Dimensional Quantum Correlations.
abstract: 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.
authors.affiliation: Department of Physics, Bilkent University, Ankara 06800, Turkey.
authors.forename: Miguel
authors.initials: M
authors.lastname: Navascués
authors.affiliation: Institute for Nuclear Research, Hungarian Academy of Sciences, P.O. Box 51, H-4001 Debrecen, Hungary.|Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland.
authors.forename: Tamás
authors.initials: T
authors.lastname: Vértesi