  Previous theoretical works showed that all pure two-qubit entangled states
can generate one bit of local randomness and can be self-tested through the
violation of proper Bell inequalities. We report an experiment in which nearly
pure partially entangled states of photonic qubits are produced to investigate
these tasks in a practical scenario. We show that small deviations from the
ideal situation make low entangled states impractical to self-testing and
randomness generation using the available techniques. Our results show that in
practice lower entanglement implies lower randomness generation, recovering the
intuition that maximally entangled states are better candidates for
deviceindependent quantum information processing.
