Unbounded randomness certification using sequences of measurements

F. J. Curchod, M. Johansson, R. Augusiak, M. J. Hoban, P. Wittek, A. Acín
2017 Physical Review A  
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)
more » ... 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.
doi:10.1103/physreva.95.020102 fatcat:bat7btizprbnxp7d6iydqui3dq