While messing around with numerical models of entangled states, I found a very simple and convenient way to characterize entanglement without a local frame of reference:

https://peteshadbolt.co.uk/posts/random_measurements/

It's the one result from my academic career that really felt rewarding. It's not a very important or mind-blowing result, but it is vaguely useful, and (to me at least) enlightening, and it is a clean, finished, self-contained piece of work. Makes me happy at least :)