@Kiro actually I think it's a good question, I was hoping someone more apt with CVs would give a good answer. My intuition is that they can perform the same overall operations to arbitrary accuracy, albeit the individual gates will look entirely different due to the different encodings. E.g. a "CNOT" will look different in CVs because you don't really have qubits to operate with. But I'm not sure how to give a more precise answer because I'm not really sure how a CNOT looks like in CVs

Oooh, that is an interesting one

@MoreAnonymous Looking at it again now, there's a lot to just sit and work through - I'm not entirely convinced that your question is a full proof, but at the same time would be totally unsurprised if this is the case

@Mithrandir24601 is there anything on what I'm calling "conditional time evolution" in the literature?

@MoreAnonymous From about 15-20 years ago, yeah, although I haven't read them

@Mithrandir24601 does it go under the same name?

@MoreAnonymous Some do - there's conditional time evolution, conditional quantum evolution, conditional gate operations... What I can't find right now is anything on the entropy of such things

@Mithrandir24601 to be fair my claim is more to do with the entropy of the environment.

@MoreAnonymous To be fair, when you doing anything like a measurement, the entropy of the environment increases

So, this does seem like something that makes sense

@Mithrandir24601 is there a proof for that though? I haven't seen one

@MoreAnonymous Not as far as I'm aware for what you've done

But the measurement one is simple - 'any time you gain info about a system, you decrease its entropy, so the entropy of the environment increases' is the gist

@Mithrandir24601 I see