The uncertainty principle sets a limit to our capacity to predict the outcomes of two incompatible measurements. The Heisenberg uncertainty relation for two arbitrary observables and is usually discussed in textbooks. However, little or no attention is paid to the fact that Schrdinger generalised the Heisenberg relation taking into account the covariance between the observables and . This extended inequality is known as the Robertson–Schrdinger uncertainty relation. Here, we demonstrate the less known fact that two-level quantum states, i.e., qubits, satisfy the equality of the Robertson–Schrdinger uncertainty relation for two arbitrary observables and . Taking advantage of the homomorphism between SU(2) and SO(3) groups, it is possible to map the distributions of the expectation values and variances of the observables, and the Heisenberg and covariance terms on the Bloch sphere. The graphical visualisation of the relevant quantities involved in the uncertainty relations allows us to distinguish specific properties and symmetries that are not so evident in the algebraic formalism.

不确定性原则限制了我们预测两个不兼容测量结果的能力。对于任意两个观测的海森堡不确定关系，并通常在教科书中讨论。但是，几乎没有或根本没有注意到Schrdinger结合了可观测量和的协方差来推广海森堡关系的事实。这种扩展的不等式被称为罗伯逊-施丁格不确定性关系。在这里，我们证明了一个鲜为人知的事实，即两级量子态（即量子位）满足两个任意可观测量的Robertson-Schrdinger不确定性关系的等式和。利用SU（2）和SO（3）组之间的同态性，可以在Bloch球上映射期望值的分布和可观测值的方差以及Heisenberg和协方差项。不确定性关系中涉及的相关量的图形化可视化使我们能够区分代数形式主义中不那么明显的特定属性和对称性。