Uncertainty Relations for Joint Localizability and Joint Measurability in Finite-Dimensional Systems

摘要

Two quantities quantifying uncertainty relations are examined. InJ.Math.Phys. 48, 082103 (2007), Busch and Pearson investigated the limitationon joint localizability and joint measurement of position and momentum byintroducing overall width and error bar width. In this paper, we show a simplerelationship between these quantities for finite-dimensional systems. Ourresult indicates that if there is a bound on joint localizability, it ispossible to obtain a similar bound on joint measurability. Forfinite-dimensional systems, uncertainty relations for a pair of generalprojection-valued measures are obtained as by-products.