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How can I take the Wigner transform of an operator with an absolute value?

I want to be able to find the Wigner transforms of operators of the form $\Theta(\hat{O})$, where $\Theta$ is the Heaviside function and $\hat{O}$ in general depends on both $x$ and $p$. For the ...
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Deriving probability distributions from the Wigner distribution

I know that I can calculate the probability distributions of $x$ and $p$ from the Wigner quasiprobability distribution, and I can calculate the probability distributions of other operators by ...
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What is the physical meaning of the “projection” of the mutual intensity function of a given signal?

Let's consider an optical wave $$\psi(t) = \psi(t, x=0)$$ Its mutual intensity function is defined as : $$ \gamma(t,\theta) := \psi(t+\theta/2).\psi(t-\theta/2) $$ So, what is the physical meaning of ...