Metrology and multipartite entanglement in measurement-induced phase transition

Giovanni Di Fresco, Bernardo Spagnolo, Davide Valenti, and Angelo Carollo

Dipartimento di Fisica e Chimica ``Emilio Segrè", Group of Interdisciplinary Theoretical Physics, Università degli studi di Palermo, Viale delle Scienze, Ed. 18, I-90128 Palermo, Italy

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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.

Measurement-induced quantum phase transitions arise from the interplay between unitary dynamics and repeated measurement processes. They manifest as an abrupt change in the entanglement properties of the monitored system as a critical measurement strength is approached. In this paper, we explore this phenomenon in the framework of quantum critical metrology, by studying the divergences of the Quantum Fisher information (QFI) near criticalities. This allows for the enhancement of quantum sensing performance, and, at the same time, it provides a characterisation of the phase transition. Here, we utilize two distinct metrological schemes. With one, we show how it is possible to reconstruct the phase diagram of the model using the QFI. With the other, we highlight the non-analyticity of the QFI.

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Cited by

[1] Sudipto Singha Roy, Soumik Bandyopadhyay, Ricardo Costa de Almeida, and Philipp Hauke, "Unveiling Eigenstate Thermalization for Non-Hermitian systems", arXiv:2309.00049, (2023).

[2] Sebastien J Avakian, T. Pereg-Barnea, and William Witczak-Krempa, "Long-range multipartite entanglement near measurement-induced transitions", arXiv:2404.16095, (2024).

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