Bounding the Set of Finite Dimensional Quantum Correlations

Date
2015
Authors
Navascués, M.
Vértesi, T.
Advisor
Instructor
Source Title
Physical Review Letters
Print ISSN
0031-9007
Electronic ISSN
Publisher
American Physical Society
Volume
115
Issue
2
Pages
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
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. © 2015 American Physical Society. © 2015 American Physical Society.

Course
Other identifiers
Book Title
Keywords
Quantum communication, Quantum optics, Finite dimensional, Finite-dimensional quantum systems, Operator algebras, Quantum communication complexity, Quantum correlations, Quantum nonlocality, Semidefinite programing, Two-level system, Quantum theory
Citation
Published Version (Please cite this version)