Uncertainties of genuinely incompatible triple measurements based on statistical distance

12 Mar 2019  ·  Qin Hui-Hui, Zhang Ting-Gui, Jost Leonardo, Sun Chang-Pu, Li-Jost Xianqing, Fei Shao-Ming ·

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. read more

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Quantum Physics