Thanks I'll keep that in mind. Honestly my motivation on working on this kind of stuff was Wigner's friend since they also seem to have a conditional time evolution there.
"From the friend's point of view, the spin has collapsed into one of its basis states upon his measurement, and hence, they will assign to the spin the state corresponding to their measurement result: If they got 0, they will assign the state ${\displaystyle |0\rangle _{S}}$ to the spin, if they got 1, they will assign the state ${\displaystyle |1\rangle _{S}}$" - wiki
"From the friend's point of view, the spin has collapsed into one of its basis states upon his measurement, and hence, they will assign to the spin the state corresponding to their measurement result: If they got 0, they will assign the state ${\displaystyle |0\rangle _{S}}$ to the spin, if they got 1, they will assign the state ${\displaystyle |1\rangle _{S}}$" - wiki
