quantum mechanics - How does many possible futures not mean many possible pasts?

The following link implies that quantum mechanics only violates the "one future" aspect of information conservation:
https://www.physicsforums.com/threads/is-information-always-conserved-in-quantum-mechanics.458985/
How is it possible that we can know that there can only be one past even though any state of any system isn't known from the previous states?