Designing elegant Bell inequalities

Elegant Bell inequality is well known for its much exploited property, being maximally violated by maximal entanglement, mutually unbiased bases, and symmetric informationally complete positive operator-valued measure elements. It is the only one with such property known so far. We present a method to construct Bell inequalities with violation feature analogous to original elegant Bell inequality in high dimension from a simple analytic quantum bound. A Bell inequality with such feature is derived in three dimension for the first time. It shows larger violation than existing Bell inequalities of similar classes while requiring arguably small number of measurements.