Topological transitions in weakly monitored free fermions

We study a free fermion model where two sets of non-commuting non-projective measurements stabilize area-law entanglement scaling phases distinct topological order. show the presence phase transition that is different universality class than observed in stroboscopic projective circuits. In unitary dynamics, topologically are separated by region with sub-volume entropy. find this well identified combination bipartite entropy and further diagram qualitatively captured an analytically tractable non-Hermitian obtained via post-selecting measurement outcome. Finally we introduce partial-post-selection continuous mapping, uniquely associates indices Hamiltonian to stochastic measurement-induced dynamics.