Can we copy information using reversible operations?

[zonde]

TL;DR

In QM interpretations discussions there is idea that classical world could be modeled using just reversible unitary evolution. But in classical world we can make copies of information. Is there any conflict between this idea and this observation?

I am trying to investigate my doubts that reversible operations can model (or at least mimic) information copy process.

For simple model I take two numbers $A \neq B$. Now I can't copy value of A into B without erasing (irreversibly) value of B. However I can use transformation that replaces value of A with new value A' such that A'=B'. That would mimic information copy process because result of copy process we verify by comparing original with copy.
But now I take third number C ($C \neq B'$) and try to copy value of B' into C. Using the same transformation as previously I replace B' with B'' such that B''=C' so that it seems I copied B into C. But now $C' \neq A'$ so the appearance of copy operation fails.
So it seems that only way how to mimic copy operation is to change all the previous copies every time a new copy is made (when I copy B' into C I have to replace A', B' and C with A'', B'' and C' such that A''=B''=C').

Does this simplified model seems universal enough to apply to any reversible transformation including QM unitary evolution?

 

[PeterDonis]

Summary: In QM interpretations discussions there is idea that classical world could be modeled using just reversible unitary evolution. But in classical world we can make copies of information. Is there any conflict between this idea and this observation?

Yes, because in quantum mechanics there is something called the no cloning theorem, which says that it is impossible to make an exact copy of a quantum state. If the dynamics of reversible unitary evolution allowed copying of information, the no cloning theorem would be violated.