  We develop an effective field theory characterizing the impact of decoherence
on states with abelian topological order and on their capacity to protect
quantum information. The decoherence appears as a temporal defect in the double
topological quantum field theory that describes the pure density matrix of the
uncorrupted state, and it drives a boundary phase transition involving anyon
condensation at a critical coupling strength. The ensuing decoherence-induced
phases and the loss of quantum information are classified by the Lagrangian
subgroups of the double topological order. Our framework generalizes the error
recovery transitions, previously derived for certain stabilizer codes, to
generic topologically ordered states and shows that they stem from phase
transitions in the intrinsic topological order characterizing the mixed state.
