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  • Open Access

Fundamental scaling limit in critical quantum metrology

Ju-Yeon Gyhm1,*, Hyukjoon Kwon2,†, and Myung-Joong Hwang3,‡

  • *Contact author: kjy3665@snu.ac.kr
  • †Contact author: hjkwon@kias.re.kr
  • ‡Contact author: myungjoong.hwang@duke.edu
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Phys. Rev. Research 8, 033004 – Published 1 July, 2026

DOI: https://doi.org/10.1103/xwlk-2zfp

Abstract

Critical quantum metrology aims to harness critical properties near quantum phase transitions to enhance parameter estimation precision. However, critical slowing down inherently limits the achievable precision within a finite evolution time. To address this challenge, we establish a fundamental scaling limit of critical quantum metrology with respect to the total evolution time. We find that the effective winding number of the system's phase-space trajectory determines the scaling bound of quantum Fisher information. Furthermore, we demonstrate that the exponential scaling of the quantum Fisher information can be obtained, and for this, it is necessary to increase the effective winding number by the total evolution time. Based on the topological nature of the effective winding number, we explicitly derive an optimal time-dependent control whose form is, surprisingly, a simple on-off scheme. We highlight that such an exponential scaling of quantum Fisher information remains valid even without reaching the critical point and in the presence of thermal dissipation, albeit with a decreased exponent.

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Outline

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Phys. Rev. Research 8, 033004– Published 1 July, 2026
  • Received 29 June 2025
  • Revised 2 February 2026
  • Accepted 17 June 2026
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