Bell nonlocality is the key quantum resource in some device-independent quantum information processing. It is of great importance to study the efficient sharing of this resource. Unsharp measurements are widely used in sharing the nonlocality of an entangled state shared among several sequential observers. Recently, the authors in [Phys. Rev. Lett. 129, 230402 (2022)] showed that the Bell nonlocality of two-qubit pure states can be shared even when one only uses projective measurements and local randomness. We demonstrate that projective measurements are also sufficient for sharing the Bell nonlocality of arbitrary high-dimensional pure bipartite states. Our results promote further understanding of the nonlocality sharing of high-dimensional quantum states under projective measurements.
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.
Combining recent advances in superconducting quantum hardware, we explore quantum correlations in a previously inaccessible regime by observing \emph{simultaneously} high-dimensional and many-body Bell non-locality. We report a high-confidence Bell violation in the correlations between two
d=64-dimensional systems encoded in twelve qubits. For system sizes up to
d=32, the strength of the observed nonlocal correlations exceeds the quantum upper bound for
d=2 systems, providing direct evidence of high-dimensional nonlocality. Furthermore, we demonstrate that the observed violation is genuinely collective: all qubits contribute to the nonlocal correlations, while most pairwise correlations across the bipartition remain Bell-local. Our work illustrates how present-day quantum processors enable the exploration of fundamental predictions of quantum mechanics in previously inaccessible regimes and, in turn, how fundamental quantum effects can be used to benchmark their performance.