I think you just assumed the result. With quantum mechanics, a and b will be different if could rollback time. Or if made the same measurement with the exact s

I think you just assumed the result. With quantum mechanics, a and b will be different if could rollback time. Or if made the same measurement with the exact same state. Quantum mechanics is indeterminate and probabilistic. Some of the most brilliant physicists like von Neumann and Bell, who won the Nobel Prize for this work, have proved it. Unless you have something that will win the Nobel Prize, your intuition is wrong. Check out https://en.wikipedia.org/wiki/Quantum_indeterminacy https://en.wikipedia.org/wiki/Quantum_indeterminacy