So, a Wigner function can be defined as the Weyl transform of the density operator. But what about the transformation from state to Wigner function? This wikipedia page suggests it might be called the Wigner map... but I might be misunderstanding.
https://en.wikipedia.org/wiki/Wigner%E2%80%93Weyl_transform

It's probably better not to lean too hard on Wikipedia. Looking at this closer, it doesn't seem very consistent. And Case isn't helping. https://aapt.scitation.org/doi/10.1119/1.2957889

Until I hear differently, I will call the transformation between operators and functions, the Weyl transform, and the transformation between states and Wigner functions, the Wigner transform. I guess there isn't really a name for going from a state to a density matrix...

Sometimes I check how many people view these conversations with myself...
For some reason, the third tweet in this thread has been much more widely seen than the other two.

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