Is information ALWAYS conserved in quantum mechanics?

[zeromodz]

I have been doing some research on Leonard Susskind and how he claims information is conserved. I don't think if we reverse time we will get back what we started EVERY single time. Thinking that information is conserved really doesn't make sense to me. What do you think? If you agree with me, could you come up with some examples. If you disagree, back it up. Thanks

 

[haael]

"Conservation of information", the Liouville's theorem, neccessarily implies determinism. QM is definitely not deterministic, as we understand it today. The unitary evolution of a quantum state is deterministic, but at the moment of collapse, new information appears.

Determinism alone is not enough to have Liouville's theorem, though. General relativity is deterministic, but information can be destroyed during creation of a black hole. The "no hair" theorem states that a black hole carries only few bits of information, forgetting about most properties of matter that had fallen into it.

The Liouville's theorem holds only if for each state there is exactly one future and exactly one past. QM violates the first, GR the latter. There are theories (like the Hawking radiation) that violate both.
Classical mechanics is perfectly deterministic and information-conserving.

The change of information capacity is an important indicator of the time arrow. It's the only microscopic process not symmetric under time reversal.

The important philosophical question: is the Liouville's theorem good or bad? Should we be happy that our current theories break information conservation, or should we seek for a better theory that preserves it?
Classical thermodynamics depends on Liouville's theorem and can not live without it.

There are theories that try to be information-preserving. I.e. there is a hypothesis that black holes actually hold some information (they have hair) that can be further extracted through the Hawking radiation.
Other theories do not have information preservation, but try to be time-reversible. The information loss in black holes is the same thing that the creation of information in quantum decays.