  We introduce a framework to decompose a bosonic mode into two virtual
subsystems-a logical qubit and a gauge mode. This framework allows the entire
toolkit of qubit-based quantum information to be applied in the
continuous-variable setting. We give a detailed example based on a modular
decomposition of the position basis and apply it in two situations. First, we
decompose Gottesman-Kitaev-Preskill grid states and find that the encoded
logical state can be damaged due to entanglement with the gauge mode. Second,
we identify and disentangle qubit cluster states hidden inside of Gaussian
continuous-variable cluster states.
