  By performing local projective measurements on a two-qubit entangled state
one can certify in a device-independent way up to one bit of randomness. We
show here that general measurements, defined by positive-operator-valued
measures, can certify up to two bits of randomness, which is the optimal amount
of randomness that can be certified from an entangled bit. General measurements
thus provide an advantage over projective ones for device-independent
randomness certification.
