Abstract We study the use of methods based on the real symplectic groups S p ( 2 n , R ) in the analysis of the Arthurs-Kelly model of proposed simultaneous measurements of position and momentum in quantum mechanics. Consistent with the fact that such measurements are in fact not possible, with arbitrary precision, we show that the observable consequences of the Arthurs-Kelly interaction term are contained in the symplectic transformation law connecting the system plus apparatus variance matrices at an initial and a final time. The individual variance matrices are made up of averages and spreads or uncertainties for single hermitian observables one at a time, which are quantum mechanically well defined. The consequences of the multimode symplectic covariant Uncertainty Principle in the Arthurs-Kelly context are examined.

中文翻译：

---

辛群方法和量子力学中的 Arthurs Kelly 测量模型

摘要 我们研究了基于实辛群 Sp ( 2 n , R ) 的方法在量子力学中提出的同时测量位置和动量的 Arthurs-Kelly 模型的分析中的使用。与此类测量实际上不可能以任意精度进行的事实一致，我们表明 Arthurs-Kelly 相互作用项的可观察结果包含在连接系统加设备方差矩阵的辛变换定律中时间。单个方差矩阵由一次一个单一厄密可观测值的平均值和散布或不确定性组成，它们在量子力学上是明确定义的。研究了 Arthurs-Kelly 上下文中多模辛协变不确定性原理的后果。