We investigate the crucial role played by a global symmetry in the purification timescales and the phase transitions of monitored free fermionic systems separating a mixed and a pure phase. Concretely, we study Majorana and Dirac circuits with ${\mathbb{Z}}_2$ and U(1) symmetries, respectively. In the first case, we demonstrate the mixed phase of $L$ sites has a purification timescale that scales as ${\tau }_P\sim LlnL$. At $1\ll t\ll {\tau }_P$ the system attains a finite residual entropy, that we use to unveil the critical properties of the purification transition. In contrast, free fermions with U(1) manifest a sublinear purification timescale at any measurement rate and an apparent Berezinskii-Kosterlitz-Thouless criticality. We find the mixed phase is characterized by ${\tau }_P\sim L^{\alpha \left(p\right)}$, with a continuously varying exponent $\alpha \left(p\right)<1$.

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• Quantum channels
• Quantum circuits
• Quantum correlations in quantum information
• Quantum measurements
• Dynamic critical phenomena