  Random numbers are an important resource for applications such as numerical
simulation and secure communication. However, it is difficult to certify
whether a physical random number generator is truly unpredictable. Here, we
exploit the phenomenon of quantum nonlocality in a loophole-free photonic Bell
test experiment for the generation of randomness that cannot be predicted
within any physical theory that allows one to make independent measurement
choices and prohibits superluminal signaling. To certify and quantify the
randomness, we describe a new protocol that performs well in an experimental
regime characterized by low violation of Bell inequalities. Applying an
extractor function to our data, we obtained 256 new random bits, uniform to
within 0.001.
