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Measurement-induced phase transition arises from the competition between adeterministic quantum evolution and a repeated measurement process. We explorethe measurement-induced phase transition through the Quantum Fisher Informationin two different metrological scenarios. We demonstrate through the scalingbehavior of the quantum Fisher information the transition of the multi-partiteentanglement across the phases. In analogy with standard quantum phasetransition, we reveal signature of a measurement-induced phase transition inthe non-analytic behaviour of the quantum Fisher information as the measurementstrength approaches the critical value. Our results offer novel insights intothe features of a quantum systems undergoing measurement-induced phasetransition and indicate potential avenues for further exploration in the fieldof quantum physics.

Metrology and multipartite entanglement in measurement-induced phase transition