Optical Wigner function
= Optical Wigner function
{title2=$W(x,y)$}
For $X_1=x$, $X_2=y$ with $[X_1,X_2]=i/2$, normalize the phase-space function by $\int W(x,y)\,dx\,dy=1$. A <coherent state> of amplitude $\alpha$ has $W=2e^{-2|x+iy-\alpha|^2}/\pi$. Quadrature marginals are physical probability distributions, but the full function can be negative. Cross terms of an <optical cat state> give interference fringes, even when low-order moments approach those of a mixture.