  We consider the problem of reversing quantum dynamics, with the goal of
preserving an initial state's quantum entanglement or classical correlation
with a reference system. We exhibit an approximate reversal operation, adapted
to the initial density operator and the ``noise'' dynamics to be reversed. We
show that its error in preserving either quantum or classical information is no
more than twice that of the optimal reversal operation. Applications to quantum
algorithms and information transmission are discussed.
