28 quED Manual www.qutools.com
The statistical nature of the inequality requires that sufficiently long integration time for
collecting the required 16 coincidence rates is chosen. Simple rule for sums is applied to
determine the standard deviation of the experimental value :
where the errors on the individual correlation coefficients are computed via Gaussian
error propagation:
where we assumed independent errors on the individual measurements and the Poisson
photon number statistics
1
. If the experimental value is numerically greater than 2 it has
violated the CHSH inequality. The strength of violation is usually defined in terms of the
number
of standard deviations which add up into the gap between the experimental value
and the local realistic bound 2:
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1
When the individual events are assumed to be independent of each other, the resulting
statistics becomes Poissonian. The variance of a Poisson distribution with mean is also .
Hence the standard deviation is
.
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