  Unpredictability, or randomness, of the outcomes of measurements made on an
entangled state can be certified provided that the statistics violate a Bell
inequality. In the standard Bell scenario where each party performs a single
measurement on its share of the system, only a finite amount of randomness, of
at most $4 log_2 d$ bits, can be certified from a pair of entangled particles
of dimension $d$. Our work shows that this fundamental limitation can be
overcome using sequences of (nonprojective) measurements on the same system.
More precisely, we prove that one can certify any amount of random bits from a
pair of qubits in a pure state as the resource, even if it is arbitrarily
weakly entangled. In addition, this certification is achieved by near-maximal
violation of a particular Bell inequality for each measurement in the sequence.
