Although "Heisenberg’s uncertainty principle’’ is represented by a rigorously proven relation about intrinsic uncertainties in quantum states, Heisenberg’s error–disturbance relation (EDR) has been commonly believed as another aspect of the principle. Based on the recent development of universally valid reformulations of Heisenberg’s EDR, we study the error and disturbance of Stern–Gerlach measurements of a spin-1/2 particle. We determine the range of the possible values of the error and disturbance for arbitrary Stern–Gerlach apparatuses with the orbital degree prepared in an arbitrary Gaussian state. We show that their error–disturbance region is close to the theoretical optimal and actually violates Heisenberg’s EDR in a broad range of experimental parameters. We also show the existence of orbital states in which the error is minimized by the screen at a finite distance from the magnet, in contrast to the standard assumption.

中文翻译：

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Stern-Gerlach测量中的误差-干扰关系

尽管“海森堡不确定性原理”以严格证明的量子态固有不确定性关系表示，但人们普遍认为海森堡的误差-干扰关系（EDR）是该原理的另一个方面。海森堡的EDR，我们研究了自旋1/2粒子的Stern-Gerlach测量的误差和扰动，并确定了任意Stern-Gerlach装置在任意轨道上准备的轨道度的误差和扰动可能值的范围高斯状态我们证明了它们的误差扰动区域接近理论最优值，并且在广泛的实验参数中实际上违反了海森堡的EDR。与标准假设相反，我们还显示了轨道状态的存在，在这种状态下，屏幕在距磁铁有限的距离处将误差最小化。