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  • Open Access

Uncertainty-disturbance relations and applications

Liang-Liang Sun1,*, Kishor Bharti2, Xiang Zhou3, Leong-Chuan Kwek4,5,6,†, Jingyun Fan7,8,9,‡, and Sixia Yu1,3,9,§

  • *Contact author: sun18@ustc.edu.cn
  • †Contact author: kwekleongchuan@nus.edu.sg
  • ‡Contact author: Fanjy@sustech.edu.cn
  • §Contact author: yusixia@ustc.edu.cn
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Phys. Rev. Research 8, 013287 – Published 17 March, 2026

DOI: https://doi.org/10.1103/q9c1-nnqj

Abstract

Uncertainty and intrinsic measurement disturbance, two fundamental concepts in quantum measurement, have conventionally been viewed as distinct and studied separately. In this work, we establish a fundamental connection between them, proving that uncertainty not only serves as a prerequisite for intrinsic disturbance but also bounds it from above. We formalize this connection via uncertainty-disturbance relations (UDRs) with direct applications in quantum information science. We show that for rank-one projective measurements, these UDRs effectively function as uncertainty relations by bounding the uncertainties of incompatible measurements. They also enable the experimental estimation of key quantum resources—including von Neumann entropy, purity, coherence, and genuine randomness. Our findings thus unify the understanding of uncertainty and disturbance and provide a versatile framework for quantum resource detection.

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Phys. Rev. Research 8, 013287– Published 17 March, 2026
  • Received 28 September 2023
  • Accepted 2 February 2026
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