Generalized Clauser-Horne-Shimony-Holt inequalities maximally violated by higher dimensional systems

Abstract

Imagine two parties, Alice and Bob who share an entangled quantum state. A well-established result that if Alice performs two-outcome measurement on the portion of the state in her possession and Bob does likewise, they are able to produce correlations that cannot be reproduced by any classical theory. The allowed classical correlations can be expressed quantitatively by the Bell inequalities. Here we propose new families of Bell inequalities, as a generalization of the Clauser-Horne-Shimony-Holt (CHSH) inequality and show that the maximum violation of these Bell inequalities allowed by quantum theory can not be attained by a bipartite quantum system having support on a qubit at each site.

8 pages, no figures, REVTeX; published version

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• More efficient Bell inequalities for Werner states
• Experimental estimation of the dimension of classical and quantum systems
• Quantum Bounds on Bell inequalities
• Bounding the dimension of bipartite quantum systems
• Device-Independent Tests of Entropy
• Device-independent certification of high-dimensional quantum systems
• Characterization of quantum correlations with local dimension constraints and its device-independent applications
• Qutrit witness from the Grothendieck constant of order four
• Testing dimension and non-classicality in communication networks
• Towards an equivalence between maximal entanglement and maximal quantum nonlocality
• Bell inequalities for three systems and arbitrarily many measurement outcomes
• Designing Bell inequalities from a Tsirelson bound
• Bell inequalities tailored to the Greenberger-Horne-Zeilinger states of arbitrary local dimension
• Concavity of the quantum body for any given dimension
• Multipartite Nonlocality as a Resource and Quantum Correlations Having Indefinite Causal Order
• Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant
• Geometrical self-testing of partially entangled two-qubit states
• Cryptographic Quantum Bound on Nonlocality
• Dimensionality Distinguishers
• Platonic Bell inequalities for all dimensions
• Better bounds on finite-order Grothendieck constants