We investigate the notion of uncertainty region using the variance based sum uncertainty relation for qubits and qutrits. We compare uncertainty region of the qubit (a 2-level system) with that of the qutrit (3-level system) by considering sum uncertainty relation for two non-commuting Pauli-like observables, acting on the two dimensional qubit Hilbert space. We identify that physically valid uncertainty region of a qubit is smaller than that of a qutrit. This implies that an enhanced precision can be achieved in the measurement of incompatible Pauli-like observables acting on the 2-dimensional subspace of a qutrit Hilbert space. We discuss the implication of the reduced uncertainties in the steady states of Λ, V, Ξ types of 3-level atomic systems. Furthermore, we construct a two-qubit permutation symmetric state, corresponding to a 3-level system and show that the reduction in the sum uncertainty value - or equivalently, increased uncertainty region of a qutrit system – is a consequence of quantum entanglement in the two-qubit system. Our results suggest that uncertainty region can be used as a dimensional witness.

我们使用基于方差的qubit和qutrit之和的不确定性关系研究不确定性区域的概念。我们比较不确定区域通过考虑作用于二维量子位希尔伯特空间的两个非交换Pauli样可观对象的和不确定性关系，来确定量子位（2级系统）与量子态（3级系统）之间的关系。我们确定，量子位的物理有效不确定性区域小于量子态的不确定性区域。这意味着在作用于qutrit Hilbert空间的二维子空间上的不兼容Pauli样可观测对象的测量中，可以实现更高的精度。我们讨论了三能级原子系统的Λ，V，Ξ类型稳态下不确定性的降低。此外，我们构造了一个对应于3级系统的2比特置换对称状态，并表明总和不确定性值的减小-或等效地，量子态系统中不确定区域的增加–是两个量子位系统中量子纠缠的结果。我们的结果表明，不确定性区域可以用作量纲见证。