> EDIT: So apparently I have to sign up for an account with yet another service, Readcube? No thanks...
I don't think so (I don't have access to nature journals so I can't check myself) but on the nature page for the article, if you click the share button it should be as a "shareable link" at the top.
This is Nature Physics, not Nature. They are separate journals, albeit under the same publishing group.
Email me (my username @gmail) if you want a copy, or look at /r/scholar.