How to show that cloning by measurement is impossible?

[greypilgrim]

Hi,

I know the common proof of the no-cloning theorem assuming the cloning apparatus acts unitarily on the system and leading this to a contradiction.

But what about a non-unitarian apparatus that involves measurements? I'm pretty sure cloning is still impossible, but I don't know how to prove it in full generality, since you could do very elaborate measurement procedures that could involve entanglement swapping or unitarily evolving parts.

Somebody knows a short proof?

 

[K^2]

Just off the top of my head, you can do the proof in MWI, where measurements are unitary, and then use equivalence of MWI and CI to say that if you can't clone a state under MWI, you can't do it under Copenhagen either.

This might not be satisfactory if you really want a full proof that takes collapse into account, but it's an easy check of validity. In general, choice of interpretation can often make a problem a lot easier if you are careful with it.