Violation of local realism with spatially multimode parametric down-conversion pumped by spatially incoherent light

We experimentally demonstrate a violation of local realism with highly spatially multimode polarization-entangled two-photon states produced by spontaneous parametric down-conversion (SPDC) pumped by a spatially incoherent light source---a light-emitting diode (LED). While existing studies have observed such a violation only by postselecting the LED-pumped SPDC photons into a single spatial detection mode, we achieve a Clauser-Horne-Shimony-Holt inequality violation of $S=2.532\ifmmode\pm\else\textpm\fi{}0.069>2$ using a spatially multimode detection setup that collects nearly 4080 SPDC spatial modes. These results indicate that coherent pump sources, such as lasers, are not required for SPDC-based entanglement generation. Our work could enable novel and practical sources of entangled photons for quantum technologies such as device-independent quantum key distribution and quantum-enhanced sensing.