Bounding the Set of Finite Dimensional Quantum Correlations
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 qu...
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| Veröffentlicht in: | Physical review letters 2015-07, Vol.115 (2), p.020501-020501, Article 020501 |
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| container_title | Physical review letters |
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| creator | Navascues, Miguel Vertesi, Tamas |
| description | 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. |
| doi_str_mv | 10.1103/PhysRevLett.115.020501 |
| format | Article |
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| ispartof | Physical review letters, 2015-07, Vol.115 (2), p.020501-020501, Article 020501 |
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| language | eng |
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| source | American Physical Society Journals |
| subjects | Algebra Bells Correlation Hilbert space Mathematical analysis Operators Optimization Quantum theory |
| title | Bounding the Set of Finite Dimensional Quantum Correlations |
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