I see, sad those potential edits will be missed from appearing in the article, still could I ask you anyways to expand about "landmark results, open problems" ?
Right that is nice point I wouldn't have think about if you hadn't draw my attention there, well that was all I will be not taking more of your time, thank you very much for answering all my doubts it was very productive for me as I learned a lot =), all the best.
I think it makes sense but I also what I said before so if these really can't be compatible then I'm still confused, what I believe is that non superposing states should be a subset of any superposed state with its corresponding computational basis state, something like:
|Simulated state |Computational basis state that allows classical simulation|
|Non entangled superposed state |product/stabilizer/fermionic state|
|Entangled superposed state |stabilizer/fermionic state|
|Magic superposed state |fermionic state|
So as I see it non superposing states are a special case of any classically simulable superposed state so they can always be classically simulated.
Would be incorrect to consider the example where there is no superposition like a special case of the island with no entanglement? Because you should be able to classically simulate superposed states as long as these are not entangled so states with no superposition should be a particular subset.
Thanks for clarifying, reading your first comment again you say that you can cook up quite easily some other examples of islands like the 3 ones in the article, for the sake of curiosity I would be interested if you could give another comment expanding on that too.
Ah I see, searching a bit I think you're referring to multipartite entanglement (https://en.wikipedia.org/wiki/Multipartite_entanglement) don't understand much from what is written there but I believe I got the gist from from your comment, thanks a lot
If circuits without T-gates have zero "magic" and circuits without swap gates have no "interactivity" then circuits without what gates will have no entanglement? can it be characterized the same way?
Don't worry I spotted your answer 4 days late. Had to read the intro to the paper to understand what you were pointing to me (in fact maybe I should have tried before asking my first question) only section 1 the rest is beyond me, if I understood right we have that,
m_1(R^2)<=1/X_f(R^2)<=1/X_f(G)<=a(G)/|G|.
What I'm not sure of is how X_f(R^2) relates to X(R^2) that is if we were to find that the chromatic number of the plane is X(R^2)=6 then what can we say about fractional chromatic number X_f(R^2)?
Hope you see this post and if not it was still super useful, thanks a lot!
Sincere question, the article as you do mentions the connection with the Hadwinger-Nelson problem too but I still don't see quite well how they are related, how could one pose them using mathematical terminology to better be able to contrast both problems and see their similarities and differences?