  We investigate cat codes that can correct multiple excitation losses and
identify two types of logical errors: bit-flip errors due to excessive
excitation loss and dephasing errors due to quantum back-action from the
environment. We show that selected choices of logical subspace and coherent
amplitude can efficiently reduce dephasing errors. The trade-off between the
two major errors enables optimized performance of cat codes in terms of
minimized decoherence. With high coupling efficiency, we show that one-way
quantum repeaters with cat codes feature drastically boosted secure
communication rate per mode compared with conventional encoding schemes, and
thus showcase the promising potential of quantum information processing with
continuous variable quantum codes.
