I haven't gotten an answer on this yet and I set up a bounty; I figured I'd link it here too in case any stats/physics people care to take a crack at it.
Evolving into 1/2 x2 + 1/2 x3 is not a quantum operation that can occur in a closed system (it requires at the very least tracing over an auxiliary qubit).
Link to the Question
I haven't gotten an answer on this yet and I set up a bounty; I figured I'd link it here too in case any stats/physics people care to take a crack at it.