Harnessing optical disorder for Bell inequalities violation
Bell inequalities are a cornerstone of quantum physics. By carefully selecting measurement bases (typically polarization), their violation certifies quantum entanglement. Such measurements are disrupted by the presence of optical disorder in propagation paths, including polarization or spatial mode mixing in fibers and through free-space turbulence. Here, we demonstrate that disorder can instead be exploited as a resource to certify entanglement via a Bell inequality test. In our experiment, one photon of a polarization-entangled pair propagates through a commercial multimode fiber that scrambles spatial and polarization modes, producing a speckle pattern, while the other photon remains with the sender. By spatially resolving the speckle intensity pattern, we naturally access a large set of random and unknown polarization projections. We show that this set is statistically sufficient to violate a Bell inequality, thereby certifying entanglement without requiring active correction techniques. Our approach provides a fundamentally new way to test Bell inequalities, eliminating the need for an explicit choice of measurement basis, and offering a practical solution for entanglement certification in real-world quantum communication channels where disorder is unavoidable.