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Quantum Randomness from Probability Estimation with Classical Side Information



Emanuel H. 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 extractable. It can be used with arbitrary, partially known and time-dependent probabilities for the random settings choices needed for certification. Furthermore, it is suitable for application to experimental configurations with low Bell violation per trial, such as current photonic loophole-free Bell tests. We formulate the framework for the general situaion where the trial probability distributions are constrained to a known convex set 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 Ref.~\cite{bierhorst:qc2017a} and tolerates adversarial settings probability biases.
Proceedings Title
QCrypt 2017 Conference Proceedings
Conference Dates
September 18-22, 2017
Conference Location
Conference Title
QCrypt 2017 Conference


Bell tests, martingales, quantum randomness generation


Knill, E. , Zhang, Y. and Bierhorst, P. (2017), Quantum Randomness from Probability Estimation with Classical Side Information, QCrypt 2017 Conference Proceedings, Cambridge, -1 (Accessed July 17, 2024)


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Created September 20, 2017, Updated May 18, 2020