Sum Uncertainty Relations: Uncertainty Regions for Qubits and Qutrits

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