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P | 11 〉 (a ′ b ′ )) estimated by sampling four multinomial distributions. As the
number of samples increases, the statistical sampling noise goes down and
√
p(1−p)
the estimates of the probabilities becomes better following σ p = .
n
• Since the experiment is subject to 1/f noise, the drift in the “true” value
of S over the course of the experiment becomes worse and worse as the
sampling time is increased.
For small sample sizes, the standard error on S is therefore limited by statistical
sampling noise, while for large sample sizes, the error will be limited by drift of S.
Thus, there will exist a certain sample size n ∗ for which the two effects become
equal and the error switches from being dominated by sampling noise to being
dominated by experimental drifts. For sample sizes smaller than n ∗ , the above
described simple-minded analysis approach is valid, while for sample sizes larger
than n ∗ , this approach can severely underestimate the standard error σ S .
To avoid having to model the statistical effects of 1/f noise on S, the data
in this thesis will be presented as a collection of several measurements of S with
individual estimates of σ S , each of which is based on data taken over short enough
periods to guarantee sample sizes smaller than n ∗ .
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