I am working through my quantum optics textbook by Grynberg, Aspect and Fabre, and this concept has tripped me up a little.
(13) is an inseparable state, whereas (15) IS separable - but they are the same state, just written using different bases. I can't get my head around how changing our basis has somehow changed what I thought to be inherent to the state.
If this is a stupid question and I need to go back in the textbook, let me know! :)