  Preserving information stored in a physical system subjected to noise can be
modeled in a communication-theoretic paradigm, in which storage and retrieval
correspond to an input encoding and output decoding, respectively. The encoding
and decoding are then constructed in such a way as to protect against the
action of a given noisy quantum channel. This paper considers the situation in
which the noise is not due to technological imperfections, but rather to the
physical laws governing the evolution of the universe. In particular, we
consider the dynamics of quantum systems under a 1+1 Robertson-Walker spacetime
and find that the noise imparted to them is equivalent to the well known
amplitude damping channel. Since one might be interested in preserving both
classical and quantum information in such a scenario, we study trade-off coding
strategies and determine a region of achievable rates for the preservation of
both kinds of information. For applications beyond the physical setting studied
here, we also determine a trade-off between achievable rates of classical and
quantum information preservation when entanglement assistance is available.
