Quantum Randomness from Probability Estimation with Classical Side Information
Emanuel Knill, Yanbao Zhang, Peter L. Bierhorst
We develop a framework for certifying randomness from Bell-test trials based on directly estimating the probability of the measurement outcomes with adaptive test supermartingales. The number of trials need not be predetermined, and one can stop performing trials as soon as the desired amount of randomness is time-dependent probabilities for the random settings choices. Furthermore, it is suitable for application to experimental configurations with low Bell violation per trial, such as current photonic loophole-free Bell tests. It is possible to adapt to changing experimental conditions. We formulate the framework for the general situation where the trial probability distributions are constrained to a known convex set. Randomness expansion is possible for many relevant configurations with logarithmic settings entropy. We implement probability estimation numerically and apply it to a representative settings-conditional outcome probability distribution from an atomic loophole-free Bell test to illustrate trade-offs between the amount of randomness, error, settings entropy, unknown settings biases, and number of trials. We then show that probability estimation yields more randomness from the loophole-free Bell-test data analyzed in arXiv::1702.05178v1 and tolerates adversarial settings probability biases.
, Zhang, Y.
and Bierhorst, P.
Quantum Randomness from Probability Estimation with Classical Side Information, Physical Review Research, [online], https://doi.org/10.1103/PhysRevResearch.2.033465
(Accessed September 25, 2023)