Unbounded randomness certification using sequences of measurements

TL;DR

This paper demonstrates that sequences of measurements on entangled qubits can certify unlimited randomness, surpassing the finite bounds of traditional Bell tests, by achieving near-maximal Bell inequality violations.

Contribution

It introduces a method to certify unlimited randomness from entangled qubits using sequences of nonprojective measurements, overcoming previous finite bounds.

Findings

Unlimited randomness can be certified from entangled qubits.

Sequences of measurements can achieve near-maximal Bell violations.

The method applies even to weakly entangled states.

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 near-maximal violation of a particular Bell inequality for each measurement in the sequence.