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  • Tutorial
  • Open Access

Critical Quantum Sensing: A Tutorial on Parameter Estimation Near Quantum Phase Transitions

George Mihailescu1,2,*, Uesli Alushi3, Roberto Di Candia3, Simone Felicetti4,5,†, and Karol Gietka6,‡

  • *Contact author: george.mihailescu96@gmail.com
  • †Contact author: simone.felicetti@cnr.it
  • ‡Contact author: karol.gietka@uibk.ac.at
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PRX Quantum 7, 020201 – Published 8 June, 2026

DOI: https://doi.org/10.1103/v7mf-yh8n

Abstract

Quantum phenomena offer the possibility of measuring physical quantities with precision beyond classical limits. However, current progress is constrained by scalability, environmental noise, and challenges in practical integration. This highlights the necessity for novel approaches. An emerging paradigm in this direction is critical quantum metrology, which harnesses the enhanced susceptibility and nonclassical correlations that naturally occur near quantum phase transitions as resources for quantum-enhanced precision. This tutorial provides a pedagogical introduction to key concepts and a detailed overview of prominent quantum sensing strategies that exploit critical phenomena in metrology. Through examples of increasing complexity, the reader is guided through various critical quantum sensing protocols applied to different critical systems. Special emphasis is placed on the optimal scaling of estimation precision with respect to fundamental resources. Finally, we discuss how critical quantum metrology extends from idealized models to realistic open-system, dissipative regimes, and strongly correlated fermionic systems, outlining both the challenges and opportunities for future quantum technologies.

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Popular Summary

Quantum technologies offer the potential to measure physical quantities with precision far beyond classical limits, but their progress is often hindered by challenges such as scalability, environmental noise, and practical implementation. To address these limitations, researchers are turning to critical quantum metrology, a novel approach that harnesses the unique properties of quantum phase transitions. Near these transitions, systems exhibit heightened sensitivity and strong quantum correlations, making them powerful tools for precision measurements. This tutorial provides a clear and accessible introduction to both parameter estimation and critical quantum metrology, making it valuable for both experts and newcomers to the field. Readers are guided through the fundamental principles of quantum phase transitions and their role in sensing, with practical examples that illustrate how these ideas can be applied to real-world systems. The tutorial also explores advanced topics, such as the effects of dissipation and strong correlations, while highlighting the opportunities and challenges for future quantum technologies. By bridging quantum metrology, many-body physics, and critical phenomena, this tutorial offers a unique perspective on a cutting-edge topic. It is designed to inspire researchers across disciplines and equip them with the tools to explore new frontiers in quantum sensing.

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PRX Quantum 7, 020201– Published 8 June, 2026
  • Received 22 October 2025
  • Revised 30 March 2026
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