Observing Bell Inequality Violation Beyond the Qubit Bound in a Spinor Bose–Einstein Condensate

Bell nonlocality is a foundational feature of quantum mechanics, representing correlations that cannot be explained by local hidden variable models. While nonlocality has been extensively studied in qubit systems, extending this to higher-dimensional multipartite systems (qudits) remains a significant challenge. This paper investigates whether a spin-1 Bose-Einstein condensate (BEC) can exhibit genuine qutrit Bell correlations that surpass the limits of qubit-based systems.

The researchers utilize a spin-1 87Rb Bose-Einstein condensate, which naturally supports three internal spin states (mF = -1, 0, +1). By exploiting spin-exchange collisions, they generate spin-nematic squeezed states in an ensemble of approximately 3.1 x 10^4 atoms. They derive a permutationally invariant Bell inequality tailored for three-outcome systems and construct a Bell witness operator based on collective spin and nematic observables. This witness allows them to distinguish between correlations achievable by qubits and those requiring higher-dimensional qutrit resources.

The experiment demonstrates a violation of the Bell inequality that significantly surpasses the bound achievable by any collection of N qubits. By monitoring the temporal evolution of the Bell witness, the authors achieve a minimum value of 0.52(7), which is well below the qubit bound of 1. This violation certifies that approximately 48% of the atoms in the condensate occupy genuine qutrit states. A control experiment, where the system is forced into a qubit-like configuration by selectively removing population from one of the modes, confirms that the observed violation is indeed due to the three-dimensional nature of the local Hilbert space.

This work establishes spinor BECs as a scalable, macroscopic platform for investigating high-dimensional quantum correlations. By demonstrating that coarse-grained collective measurements are sufficient to certify the dimensionality of quantum states, the study provides a practical pathway for validating complex many-body resources. These findings have implications for device-independent quantum information protocols and deepen our understanding of the boundary between simple two-level quantum systems and the richer, nonlocal structures present in interacting multilevel systems.