Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks

Understand

We investigate measurement-induced phase transitions in the Quantum Ising chain coupled to a monitoring environment.

• We compare two different limits of the measurement problem, the stochastic quantum-state diffusion protocol corresponding to infinite small jumps per unit of time and the no-click limit, corresponding to post-selection and described by a non-Hermitian Hamiltonian.
• In both cases we find a remarkably similar phenomenology as the measurement strength $\gamma$ is increased, namely a sharp transition from a critical phase with logarithmic scaling of the entanglement to an area-law phase, which occurs at the same value of the measurement rate in the two protocols.
• An effective central charge, extracted from the logarithmic scaling of the entanglement, vanishes continuously at the common transition point, although with different critical behavior possibly suggesting different universality classes for the two protocols.