Testing a continuous-variable Bell-like inequality with a hybrid-encoded system

Continuous-variable quantum systems are promising candidates for quantum computing and quantum information processing. It is widely known that quadrature measurements on Gaussian continuous-variable systems can be described by a noncontextual hidden-variable model and cannot violate a Bell inequality. Here, we demonstrate that the observation fails when sequential measurements are involved. Our experiment is realized by mapping the spatial modes of a single photon, deterministically generated from an InAs/GaAs quantum emitter, to the logical operations in the Gottesman--Kitaev--Preskill code space. Employing a black-box-style approach, we observe a violation of the Bell-like noncontextual hidden-variable inequality by 380 standard deviations. Our results address the conceptual loopholes in previous works and open up new possibilities for studying fundamental quantum physics using photonic-encoded continuous-variable systems.