Browsing by Subject "Finite-dimensional quantum systems"

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    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.
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    Characterizing finite-dimensional quantum behavior
    (American Physical Society, 2015) Navascués, M.; Feix, A.; Araújo, M.; Vértesi, T.
    We study and extend the semidefinite programming (SDP) hierarchies introduced in Navascués and Vértesi [Phys. Rev. Lett. 115, 020501 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.020501] for the characterization of the statistical correlations arising from finite-dimensional quantum systems. First, we introduce the dimension-constrained noncommutative polynomial optimization (NPO) paradigm, where a number of polynomial inequalities are defined and optimization is conducted over all feasible operator representations of bounded dimensionality. Important problems in device-independent and semi-device-independent quantum information science can be formulated (or almost formulated) in this framework. We present effective SDP hierarchies to attack the general dimension-constrained NPO problem (and related ones) and prove their asymptotic convergence. To illustrate the power of these relaxations, we use them to derive a number of dimension witnesses for temporal and Bell-type correlation scenarios, and also to bound the probability of success of quantum random access codes. © 2015 American Physical Society.