Structure of the set of quantum correlators via semidefinite programming
arXiv:1809.10886 · doi:10.1103/PhysRevA.99.052108
Abstract
Quantum information leverages properties of quantum behaviors in order to perform useful tasks such as secure communication and randomness certification. Nevertheless, not much is known about the intricate geometric features of the set quantum behaviors. In this paper we study the structure of the set of quantum correlators using semidefinite programming. Our main results are (i) a generalization of the analytic description by Tsirelson-Landau-Masanes, (ii) necessary and sufficient conditions for extremality and exposedness, and (iii) an operational interpretation of extremality in the case of two dichotomic measurements, in terms of self-testing. We illustrate the usefulness of our theoretical findings with many examples and extensive computational work.
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Cited by in corpus (8)
- Robust self-testing of quantum systems via noncontextuality inequalities
- Quantum Correlations in the Minimal Scenario
- Graph-Theoretic Framework for Self-Testing in Bell Scenarios
- All tight correlation Bell inequalities have quantum violations
- Geometry of the set of synchronous quantum correlations
- Certifying nonlocal properties of noisy quantum operations
- The membership problem for constant-sized quantum correlations is undecidable
- SOS decomposition for general Bell inequalities in two qubits systems and its application to quantum randomness