论文标题
量子力学中的符号群方法和Arthurs Kelly测量模型
Symplectic group methods and the Arthurs Kelly model of measurement in quantum mechanics
论文作者
论文摘要
我们研究了基于实际符号组$ sp（2n，\ mathcal {r}）$的方法的使用，以分析量子力学中提议的同时测量的Arthurs-Kelly模型。与实际上不可能进行的测量值一致，我们表明，亚瑟 - 凯利相互作用项的可观察后果包含在连接系统加上设备方差矩阵的符号转换定律中，最初和最后一次。单个差异矩阵由一次单个Hermitian观测值的平均值和扩展或不确定性组成，它们在机械上定义得很好。检查了多模象征协变量的不确定性原理在Arthurs-Kelly上下文中的后果。
We study the use of methods based on the real symplectic groups $Sp(2n,\mathcal{R})$ 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, 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.
