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Uncertainty relations for joint localizability and joint measurability in finite-dimensional systems

机译:有限维系统中联合定位性和联合可测量性的不确定性关系

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Two quantities quantifying uncertainty relations are examined. Busch and Pearson [J. Math. Phys. 48, 082103 (2007)] investigated the limitation on joint localizability and joint measurement of position and momentum by introducing overall width and error bar width. In this paper, we show a simple relationship between these quantities for finite-dimensional systems. Our result indicates that if there is a bound on joint localizability, it is possible to obtain a similar bound on joint measurability. For finite-dimensional systems, uncertainty relations for a pair of general projection-valued measures are obtained as by-products.
机译:检查量化不确定性关系的两个量。布希和皮尔逊[J.数学。物理48,082103(2007)]通过引入整体宽度和误差线宽度,研究了关节可定位性以及位置和动量的关节测量的局限性。在本文中,我们为有限维系统显示了这些数量之间的简单关系。我们的结果表明,如果对联合可定位性存在限制,则有可能获得对联合可测量性的类似限制。对于有限维系统,作为副产品获得了一对一般投影值测度的不确定性关系。

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