Uncertainties of genuinely incompatible triple measurements based on statistical distance

Hui-Hui Qin, Ting-Gui Zhang, Leonardo Jost, Chang-Pu Sun, Xianqing Li-Jost, and Shao-Ming Fei

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Submission date: 13. Jul. 2019
Pages: 8
published in: Physical review / A, 99 (2019) 3, art-no. 032107 
DOI number (of the published article): 10.1103/PhysRevA.99.032107
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Abstract:
We investigate the measurement uncertainties of a triple of positive operator-valued measures (POVMs) based on statistical distance, and formulate state-independent tight uncertainty inequalities satisfied by the three measurements in terms of triple-wise joint measurability. Particularly, uncertainty inequalities for three unbiased qubit measurements are presented with analytical lower bounds which relates to the necessary and sufficient condition of the triple-wise joint measurability of the given triple. We show that the measurement uncertainties for a triple measurement are essentially different from the ones obtained by pair wise measurement uncertainties by comparing the lower bounds of different measurement uncertainties.