  One of the striking properties of quantum mechanics is the occurrence of the
Bell-type non-locality. They are a fundamental feature of the theory that
allows two parties that share an entangled quantum system to observe
correlations stronger than possible in classical physics. In addition to their
theoretical significance, non-local correlations have practical applications,
such as device-independent randomness generation, providing private
unpredictable numbers even when they are obtained using devices derived by an
untrusted vendor. Thus, determining the quantity of certifiable randomness that
can be produced using a specific set of non-local correlations is of
significant interest. In this paper, we present an experimental realization of
recent Bell-type operators designed to provide private random numbers that are
secure against adversaries with quantum resources. We use semi-definite
programming to provide lower bounds on the generated randomness in terms of
both min-entropy and von Neumann entropy in a device-independent scenario. We
compare experimental setups providing Bell violations close to the Tsirelson's
bound with lower rates of events, with setups having slightly worse levels of
violation but higher event rates. Our results demonstrate the first experiment
that certifies close to two bits of randomness from binary measurements of two
parties.
