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Quantum Violation: Beyond Clauser-Horne-Shimony-Holt Inequality
The best upper bound for the violation of the Clauser-Horne-Shimony-Holt
(CHSH) inequality was first derived by Tsirelson. For increasing number of valued observables on both sites of the correlation experiment, Tsirelson
obtained the Grothendieck's constant () as
a limit for the maximal violation. In this paper, we construct a generalization
of the CHSH inequality with four valued observables on both sites of a
correlation experiment and show that the quantum violation approaching 1.58.
Moreover, we estimate the maximal quantum violation of a correlation experiment
for large and equal number of valued observables on both sites. In this
case, the maximal quantum violation converges to for very
large , which coincides with the approximate value of Grothendieck's
constant.Comment: 6 page