title: Experimental Test of Heisenberg's Measurement Uncertainty Relation Based on Statistical Distances.
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.
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Wenchao
authors.initials: W
authors.lastname: Ma
authors.affiliation: Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China.
authors.forename: Zhihao
authors.initials: Z
authors.lastname: Ma
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Hengyan
authors.initials: H
authors.lastname: Wang
authors.affiliation: Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, Zhejiang 310014, China.
authors.forename: Zhihua
authors.initials: Z
authors.lastname: Chen
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Ying
authors.initials: Y
authors.lastname: Liu
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Fei
authors.initials: F
authors.lastname: Kong
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.|Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Zhaokai
authors.initials: Z
authors.lastname: Li
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.|Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Xinhua
authors.initials: X
authors.lastname: Peng
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.|Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Mingjun
authors.initials: M
authors.lastname: Shi
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.|Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Fazhan
authors.initials: F
authors.lastname: Shi
authors.affiliation: School of Mathematical Sciences, Capital Normal University, Beijing 100048, China.
authors.forename: Shao-Ming
authors.initials: SM
authors.lastname: Fei
authors.affiliation: Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.|Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Jiangfeng
authors.initials: J
authors.lastname: Du