Quantum Random Number Generation by Christian Kollmitzer & Stefan Schauer & Stefan Rass & Benjamin Rainer

Author:Christian Kollmitzer & Stefan Schauer & Stefan Rass & Benjamin Rainer
Language: eng
Format: epub
ISBN: 9783319725963
Publisher: Springer International Publishing

A simple criterion to check whether the runs test needs not to be performed is if , where . The test statistic for the runs test is given by

which is just counting the run of 0s or 1s. The reference distribution is and the p-value is computed by .

(iii)The cumulative sums test operates on the bit level and we, again, transform the bits to values in by . Then, the partial cumulative sums are computed by (forward) or (backward). The test statistics is given by or , the reference distribution is a normal distribution and the (asymptotic) p-value is computed by

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