Preserving information from the beginning to the end of time in a Robertson-Walker spacetime

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.