Uncertainties of genuinely incompatible triple measurements based on statistical distance
Huihui Qin, Ting-Gui Zhang, Leonardo Jost, Chang-Pu Sun, Xianqing Li‐Jost, Shao-Ming Fei · Physical Review A · 2019
We investigate the measurement uncertainties of a triple of positive-operator-valued measures based on statistical distance and formulate state-independent tight uncertainty inequalities satisfied by the three measurements in terms of triplewise joint measurability. In particular, uncertainty inequalities for three unbiased qubit measurements are presented with analytical lower bounds which relates to the necessary and sufficient condition of the triplewise joint measurability of the given triple. We show that the measurement uncertainties for a triple measurement are essentially different from the ones obtained by pairwise measurement uncertainties by comparing the lower bounds of different measurement uncertainties.