Hey,
sorry for going back to this topic, but the question seems relevant here.
In the example of the Purification the initial maximally mixed state is:
rho = MPO(s, "Id") ./ √2
Can it be that there is a mistake ? because the Tr(\rho)=4. On the other hand is you remove the \sqrt2 and replace it with 2 you will get Tr(\rho)=1 . but the norm will change so I am kind of confused. Maybe someone knows what is the reason, and explanation for that ?
Another question I have on this topic is if I want to change the last site so it won’t be a maximally mixed, but something else.
I want the last site will be just |\psi \rangle=\frac{1}{\sqrt2}(|0 \rangle +|1 \rangle) and \rho[end]=|\psi \rangle \langle \psi|.
I thought that we only need to take the maximally mixed state and chance the tensor elements for that site to be 0.5 in each element. Is that correct ?