Detection of nonlocality for high-dimensional quantum states via dimensional reduction

Abstract

This paper investigates the problem of nonlocality detection for high-dimensional quantum states. To overcome the complexity of measurement settings and Bell-operator optimization in high-dimensional systems, we propose a nonlocality detection framework based on dimensional reduction and chained Bell inequalities. By employing local projection operators, arbitrary high-dimensional bipartite quantum states are mapped onto effective two-qubit subsystems. We prove that if any projected subsystem violates a chained Bell inequality, then the original high-dimensional quantum state must be nonlocal. Furthermore, the framework is generalized to multipartite quantum systems. By projecting multipartite high-dimensional states onto effective multiqubit states and applying Svetlichny inequalities, sufficient criteria for detecting genuine multipartite nonlocality are established. Our approach significantly reduces the complexity of nonlocality detection in high-dimensional systems and provides a scalable theoretical framework for studying nonlocal correlations in complex quantum systems.