Measurement-induced phase transition arises from the competition between a deterministic quantum evolution and a repeated measurement process. We explore the measurement-induced phase transition through the Quantum Fisher Information in two different metrological scenarios. We demonstrate through the scaling behavior of the quantum Fisher information the transition of the multi-partite entanglement across the phases. In analogy with standard quantum phase transition, we reveal signature of a measurement-induced phase transition in the non-analytic behaviour of the quantum Fisher information as the measurement strength approaches the critical value. Our results offer novel insights into the features of a quantum systems undergoing measurement-induced phase transition and indicate potential avenues for further exploration in the field of quantum physics.

中文翻译：

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测量引起的相变中的计量学和多部分纠缠

测量引起的相变是由确定性量子演化和重复测量过程之间的竞争产生的。我们通过量子费希尔信息在两种不同的计量场景中探索测量引起的相变。我们通过量子费希尔信息的标度行为证明了多部分纠缠跨相的转变。与标准量子相变类似，当测量强度接近临界值时，我们揭示了量子费希尔信息的非解析行为中测量引起的相变的特征。我们的研究结果为经历测量引起的相变的量子系统的特征提供了新颖的见解，并指出了量子物理领域进一步探索的潜在途径。