[rich_sasha]

Especially since, isn't this an average / error of a mean estimate? So even if individual observations are non-normal, this would be a perfect place for Central Limit Theorem.

I know nothing about Quantum though, only maths.

[freemint]

Because it's a non-linear world? And the graphs seem very obviously skewed? And it's kurtosis also seems to differ from three?

[rich_sasha]

None of those things matter to the central limit theorem.

If I have IID observations with finite 2nd moment (variance), then their average will pretty quickly converge to a Gaussian distribution. And I can relax a lot of this and still recover a variant of CLT.

Of course maybe the calculation is different, eg it’s not like there are N independent observations, but rather some other complex condition solved for the mean estimate.