Uncertainties of genuinely incompatible triple measurements based on statistical distance
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.
Keywords
Cite
@article{arxiv.1903.04685,
title = {Uncertainties of genuinely incompatible triple measurements based on statistical distance},
author = {Hui-Hui Qin and Ting-Gui Zhang and Leonardo Jost and Chang-Pu Sun and Xianqing Li-Jost and Shao-Ming Fei},
journal= {arXiv preprint arXiv:1903.04685},
year = {2019}
}
Comments
6 pages, 2 figures