<i>Ab initio</i> experimental violation of Bell inequalities

The violation of a Bell inequality is the paradigmatic example device-independent quantum information: nonclassicality data certified without knowledge functioning devices. In practice, however, all experiments rely on precise understanding underlying physical mechanisms. Given that, it natural to ask: Can one witness nonclassical behavior in truly black-box scenario? Here, we propose and implement, computationally experimentally, solution this ab initio task. It exploits robust automated optimization approach based stochastic Nelder-Mead algorithm. Treating preparation measurement devices as black boxes, relying observed statistics only, our adaptive protocol approaches optimal after limited number iterations for variety photonic states, responses, scenarios. particular, exploit randomness certification from unknown states measurements. Our results demonstrate power algorithms, opening venue experimental implementation technologies.