Experimental Test of Heisenberg’s Measurement Uncertainty Relation Based on Statistical Distances

Wenchao Ma, Zhihao Ma, Hengyan Wang, Zhihua Chen, Ying Liu, Fei Kong, Zhaokai Li, Xinhua Peng, Mingjun Shi, Fazhan Shi, Shao-Ming Fei, and Jiangfeng Du
Phys. Rev. Lett. 116, 160405 – Published 22 April 2016
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Abstract

Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg’s original formulation of the uncertainty principle. Recently, Busch, Lahti, and Werner proposed inaccuracy trade-off relations based on statistical distances between probability distributions of measurement outcomes [P. Busch et al., Phys. Rev. Lett. 111, 160405 (2013); P. Busch et al., Phys. Rev. A 89, 012129 (2014)]. Here we reformulate their theoretical framework, derive an improved relation for qubit measurement, and perform an experimental test on a spin system. The relation reveals that the worst-case inaccuracy is tightly bounded from below by the incompatibility of target observables, and is verified by the experiment employing joint measurement in which two compatible observables designed to approximate two incompatible observables on one qubit are measured simultaneously.

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  • Received 23 December 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.160405

© 2016 American Physical Society

Physics Subject Headings (PhySH)

General Physics

Authors & Affiliations

Wenchao Ma1, Zhihao Ma2, Hengyan Wang1, Zhihua Chen3, Ying Liu1, Fei Kong1, Zhaokai Li1,4, Xinhua Peng1,4, Mingjun Shi1,4, Fazhan Shi1,4, Shao-Ming Fei5, and Jiangfeng Du1,4,*

  • 1Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
  • 2Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China
  • 3Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, Zhejiang 310014, China
  • 4Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
  • 5School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

  • *djf@ustc.edu.cn

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Issue

Vol. 116, Iss. 16 — 22 April 2016

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