Designing generalized elegant Bell inequalities in higher dimensions from a Tsirelson bound

TL;DR

This paper introduces a method to construct generalized Bell inequalities in higher dimensions that exhibit maximal violation properties similar to the elegant Bell inequality, including a new three-dimensional case with larger violations.

Contribution

A novel analytic approach to derive higher-dimensional Bell inequalities with maximal violation features, including the first three-dimensional example with enhanced violation.

Findings

Derived a generalized Bell inequality in three dimensions with larger violation.

Presented a systematic method for constructing Bell inequalities with elegant violation features.

Achieved larger violations with fewer measurements compared to existing inequalities.

Abstract

Elegant Bell inequality is well known for its distinctive property, being maximally violated by maximal entanglement, mutually unbiased bases, and symmetric informationally complete positive operator-valued measure elements. Despite its significance in quantum information theory demonstrated based on its unique violation feature, it remains the only known one with the characteristic. We present a method to construct Bell inequalities with violation feature analogous to elegant Bell inequality in higher local dimensions from a simple, analytic quantum bound. A Bell inequality with the generalized violation feature is derived in three dimension for the first time. It exhibits larger violation than existing Bell inequalities of similar classes, including the original elegant Bell inequality, while requiring arguably small number of measurements.