Generalizing Tsirelson's Bound on Bell Inequalities Using a Min-Max Principle

Bounds on the norm of quantum operators associated with classical Bell-type inequalities can be derived from their maximal eigenvalues. This quantitative method enables detailed predictions of the maximal violations of Bell-type inequalities.

Figure 1

Eigenvalues of $O_{33}$ in dependence of the relative angle $\theta$.

Figure 2

Maximum violation of the operator $O_{mm}$ for $m=2,\dots ,6$ for a symmetric measurement setup; the longer dashes indicate larger $m$.