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

Wenchao Ma, Zhi-Hao Ma, Hengyan Wang, Zhi-Hua Chen, Ying Liu, Fei Kong, Zhaokai Li, Xinhua Peng, Mingjun Shi, Fazhan Shi, Shao-Ming Fei, and Jiangfeng Du

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Submission date: 11. Jul. 2016
Pages: 16
published in: Physical review letters, 116 (2016), art-no. 160405 
DOI number (of the published article): 10.1103/PhysRevLett.116.160405
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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 [Phys. Rev. Lett. 111, 160405 (2013); 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.