Nonclassicality of pure two-qutrit entangled states

TL;DR

This paper conducts a comprehensive numerical study of how pure two-qutrit entangled states violate local realism, revealing that certain states with Schmidt rank-2 exhibit the most noise-robust violations, especially in higher dimensions.

Contribution

It provides the first exhaustive numerical analysis of local realism violations across all pure two-qutrit states, highlighting the robustness of Schmidt rank-2 states.

Findings

Schmidt rank-2 states show the strongest noise-robust violations.

Violations are maximized when measurement bases are optimized over all local unitaries.

Higher-dimensional systems also exhibit pronounced violations for specific states.

Abstract

We report an exhaustive numerical analysis of violations of local realism by two qutrits in all possible pure entangled states. In Bell type experiments we allow any pairs of local unitary U(3) transformations to define the measurement bases. Surprisingly, Schmidt rank-2 states, resembling pairs of maximally entangled qubits, lead to the most noise-robust violations of local realism. The phenomenon seems to be even more pronounced for four and five dimensional systems, for which we tested a few interesting examples.