Entanglement Phase Transitions in the Monitored Kitaev Model Under Perturbations

We study measurement-only monitored circuits built from the Kitaev honeycomb model and probe how local projective parity checks that do or do not respect flux conservation restructure the entanglement phases. In a stochastic protocol, single-qubit magnetic-field–type checks that do not commute with plaquette operators drive the steady state from the critical law regime to a volume-law phase at intermediate rates and finally to a trivial product state. On the other hand, the area law phase, upon being perturbed by the single site checks, stays protected until a critical rate. A three-qubit, time-reversal–breaking check that commutes with the flux operators, motivated by the chiral interaction that gaps the Kitaev spectrum to a non-Abelian spin liquid, has the opposite effect: within the same measurement-only framework, it stabilizes the critical-law phase against the short ranged area-law entanglement. By contrast, a commuting four-qubit check that simultaneously measures two opposite same-flavor bonds on a hexagon generates a distinct volume-law phase that preserves the plaquette fluxes and associated topological order, yielding extensive entanglement without erasing topological memory. We locate phase boundaries using stabilizer (Clifford) simulations together with tripartite mutual information and dynamical purification diagnostics.