Unbounded randomness certification using sequences of measurements
Abstract
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 nearmaximal violation of a particular Bell inequality for each measurement in the sequence.
 Publication:

arXiv eprints
 Pub Date:
 October 2015
 arXiv:
 arXiv:1510.03394
 Bibcode:
 2015arXiv151003394C
 Keywords:

 Quantum Physics
 EPrint:
 4 + 5 pages (1 + 3 images), published version