How can information be conserved if we live in a quantum universe?

[zeromodz]

For example, after the big bang, the only thing that decides the future is Newtons laws. However, we must take into account quantum effects we cannot be for sure what the future holds. Doesn't the same thing apply with information. How can we know the information about a system if there is quantum uncertainty?

 

[Drakkith]

Classical physics, including Newtons laws, are known to be incorrect. (or at least inaccurate) As such the future is NOT decided by Newtons laws.

 

[jmd_dk]

Physicists speaks of two kinds of information; classical information (appropriate in a Newtonian world picture) and quantum information (appropriate in the real world). Conservation of quantum information is at the heart of physics.

How can we know the information about a system if there is quantum uncertainty?

You'r right; we can't (always) know the information about a system, because of quantum uncertainties. But here nature gets weird: If we (that is, none, however technically advanced) cannot know the information about a system, then the information isn't there! It simply isn't defined. For example:
The information about exactly where an electron is, doesn't exist.
The information about where the electron certainly isn't do exist, and is conserved. That is to say that in the future, the electron won't be at a position where you know with certainty that it can't be (which sounds reasonable enough...).

Information is not an easy concept.