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

Understand

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.