Multi-setting Bell inequality for qudits

TL;DR

This paper introduces a new Bell inequality for two qutrits with three measurement settings each, showing maximal violation with mutually unbiased measurements and maximally entangled states, extending to prime dimensions.

Contribution

It proposes a generalized Bell inequality for high-dimensional systems, highlighting conditions for maximal violation and extending the concept to arbitrary prime dimensions.

Findings

Maximal violation occurs with mutually unbiased measurements and maximally entangled states.

The inequality differs from previous high-dimensional Bell inequalities.

Extension to arbitrary prime-dimensional systems is discussed.

Abstract

We propose a generalized Bell inequality for two three-dimensional systems with three settings in each local measurement. It is shown that this inequality is maximally violated if local measurements are configured to be mutually unbiased and a composite state is maximally entangled. This feature is similar to Clauser-Horne-Shimony-Holt inequality for two qubits but is in contrast with the two types of inequalities, Collins-Gisin-Linden-Massar-Popescu and Son-Lee-Kim, for high-dimensional systems. The generalization to aribitrary prime-dimensional systems is discussed.