A sum-of-squares decomposition method systematically derives Tsirelson bounds for high-dimensional quantum systems and recovers known results for qubits and qudits while finding novel bounds.
Bell inequalities for arbitrarily high dimensional systems
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abstract
We develop a novel approach to Bell inequalities based on a constraint that the correlations exhibited by local realistic theories must satisfy. This is used to construct a family of Bell inequalities for bipartite quantum systems of arbitrarily high dimensionality which are strongly resistant to noise. In particular our work gives an analytic description of numerical results of D. Kaszlikowski, P. Gnacinski, M. Zukowski, W. Miklaszewski, A. Zeilinger, Phys. Rev. Lett. {\bf 85}, 4418 (2000) and T. Durt, D. Kaszlikowski, M. Zukowski, quant-ph/0101084, and generalises them to arbitrarily high dimensionality.
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Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.
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Systematic derivation of Tsirelson bounds in arbitrary dimensions
A sum-of-squares decomposition method systematically derives Tsirelson bounds for high-dimensional quantum systems and recovers known results for qubits and qudits while finding novel bounds.
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Entanglement Certification $-$ From Theory to Experiment
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.