Unbounded randomness certification using sequences of measurements

Understand

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.