  The theory of relativity requires that no information travel faster than
light, whereas the unitarity of quantum mechanics ensures that quantum
information cannot be cloned. These conditions provide the basic constraints
that appear in information replication tasks, which formalize aspects of the
behavior of information in relativistic quantum mechanics. In this article, we
provide continuous variable (CV) strategies for spacetime quantum information
replication that are directly amenable to optical or mechanical implementation.
We use a new class of homologically-constructed CV quantum error correcting
codes to provide efficient solutions for the general case of information
replication. As compared to schemes encoding qubits, our CV solution requires
half as many shares per encoded system. We also provide an optimized five-mode
strategy for replicating quantum information in a particular configuration of
four spacetime regions designed not to be reducible to previously performed
experiments. For this optimized strategy, we provide detailed encoding and
decoding procedures using standard optical apparatus and calculate the recovery
fidelity when finite squeezing is used. As such we provide a scheme for
experimentally realizing quantum information replication using quantum optics.
