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

Abstract

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 the effects of Gaussian correlations are instead probed using Hadamard tests. 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.