Browsing by Subject "Operator algebras"

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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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    Quantum canonical transformations in star-product formalism
    (IOP, 2013) Dereli, T.; Hakioğlu, Tuğrul; Temen, A.
    We study construction of the star-product version of three basic quantum canonical transformations which are known as the generators of the full canonical algebra. By considering the fact that star-product of c-number phase-space functions is in complete isomorphism to Hilbert-space operator algebra, it is shown that while the constructions of gauge and point transformations are immediate, generator of the interchanging transformation deforms this isomorphism. As an alternative approach, we study all of them within the deformed form. How to transform any c-number function under linear-nonlinear transformations and the intertwining method are shown within this argument as the complementary subjects of the text.