From Entanglement to Work Statistics: Signatures of Measurement-Induced Transitions in No-Click Dynamics
Quantum systems under continuous monitoring exhibit a competition between coherent dynamics and measurement back-action. Focusing on the post-selected no-click limit, where no measurement events are detected, the dynamics are described by an effective non-Hermitian Hamiltonian. Using the transverse-field Ising chain, we find that increasing the measurement rate drives a phase transition between a phase with logarithmic entanglement scaling and a gapless imaginary spectrum, and a phase with area-law entanglement and a finite imaginary gap. This transition remains robust against the introduction of chaos in the system through certain interaction and symmetry-breaking perturbations but depends on the measurement basis. Extending thermodynamic analysis to no-click dynamics shows that measurements can saturate the system’s energy, suppress work fluctuations, and leave clear signatures in work statistics. These results reveal a direct connection between measurement-induced entanglement transitions and non-equilibrium thermodynamic behaviour in monitored quantum systems.
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