The paper explores the unconventional phase transitions in topological phases of matter driven by anyon condensation, particularly in the context of the toric code. The authors investigate the effects of errors that promote the proliferation of anyons with non-trivial mutual statistics. Using the triangle inequality, they show that under the presence of electromagnetic duality and partial-transpose symmetry, any phase transition out of the topological phase must deviate from standard anyon condensation rules. Specifically, they consider a self-dual quantum channel where Kraus operators are proportional to \(X + Z\). They find that the topological phase remains stable up to the maximal error rate when the density matrix is viewed as a pure state in the double Hilbert space. To access an unconventional transition, they perturb the toric code with the self-dual channel and find numerical evidence that beyond a critical error rate, the topological phase is destroyed, leading to a critical phase where anyons are only power-law condensed. The paper also discusses the constraints on anyon condensation from self-dual symmetry and partial-transpose symmetry, and maps the mixed-state transition to a statistical mechanics problem, revealing a Berezinskii–Kosterlitz–Thouless (BKT) transition at the maximum error rate.The paper explores the unconventional phase transitions in topological phases of matter driven by anyon condensation, particularly in the context of the toric code. The authors investigate the effects of errors that promote the proliferation of anyons with non-trivial mutual statistics. Using the triangle inequality, they show that under the presence of electromagnetic duality and partial-transpose symmetry, any phase transition out of the topological phase must deviate from standard anyon condensation rules. Specifically, they consider a self-dual quantum channel where Kraus operators are proportional to \(X + Z\). They find that the topological phase remains stable up to the maximal error rate when the density matrix is viewed as a pure state in the double Hilbert space. To access an unconventional transition, they perturb the toric code with the self-dual channel and find numerical evidence that beyond a critical error rate, the topological phase is destroyed, leading to a critical phase where anyons are only power-law condensed. The paper also discusses the constraints on anyon condensation from self-dual symmetry and partial-transpose symmetry, and maps the mixed-state transition to a statistical mechanics problem, revealing a Berezinskii–Kosterlitz–Thouless (BKT) transition at the maximum error rate.