adobe photoshop - Turning pixel brightness into transparency in single-hue image

I'm looking for a way to take single-hue images and turn their brightness into opacity in Photoshop.

At the simplest, say you have a flat green circle on a white background (as an already saved file). I want to turn the aliased edges where the pixels are a lighter green into pixels of the same value as the center of the circle, but more transparent.

Theoretically, I could then put this image on any color background and it would look aliased. No little borders that are so indicative of the image originally having a different background color.

This seems like a super-basic thing to do, and I'm maybe I'm just not describing it with the right words, but I can't find it ANYWHERE.

Thanks!