  A topological phase can undergo a phase transition driven by anyon
condensation. A potential obstruction to such a mechanism could arise if there
exists a symmetry between anyons that have non-trivial mutual statistics. Here
we consider toric code subjected to errors that tend to proliferate anyons with
non-trivial mutual statistics. Using triangle inequality, we show that in the
presence of electromagnetic duality and a partial-transpose symmetry, a
decoherence induced phase transition out of the topological phase must be
rather unconventional and lie beyond standard rules of anyon condensation. To
explore such physics, we first subject toric code to a self-dual quantum
channel where Kraus operators are proportional to X+Z. We find that the
topological phase is stable up to the maximal error rate, when viewing density
matrix as a pure state in the double Hilbert space. To access an unconventional
transition, we then consider a perturbed toric code subjected to the self-dual
channel, and find numerical evidence that beyond a critical error rate, the
topological phase is destroyed resulting in a critical phase where anyons are
only power-law condensed.
