Post-Selected Criticality of Measurement-Induced Phase Transitions

We investigate the post-selected critical properties of Measurement-induced phase transitions (MIPTs) in two distinct models: a monitored random quantum circuit and a random tensor network. The monitored random quantum circuit consists of two-qubit Haar-random gates and randomly interspersed post-selective projective measurements, with qubits consistently projected onto the ground state. The random tensor network model is constructed from a projected entangled pair state (PEPS) wavefunction, in which qutrits are gradually projected onto the ground state by reducing the bond dimension of the entangled pair states.

Both models exhibit a novel transition from area-law to volume-law entanglement scaling. Our numerical results provide strong evidence that these post-selected systems belong to the same universality class, distinct from that of MIPTs with non-selective measurements. Furthermore, we find that the effective central charge of the post-selected MIPT is negative, which can be attributed to the weighting of quantum trajectories in both models. These findings offer deeper insights into the influence of post-selection on the entanglement properties of quantum systems.