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arXiv · 2101.11545

Sum Uncertainty Relations: Uncertainty Regions for Qubits and Qutrits

Seeta Vasudevrao·I. Reena·Sudha·A. R. Usha Devi·A. K. Rajagopal
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Abstract

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 Lambda, V and Cascade 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.

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Seeta Vasudevrao, I. Reena, Sudha, A. R. Usha Devi, A. K. Rajagopal. 2021-01-27. Sum Uncertainty Relations: Uncertainty Regions for Qubits and Qutrits. https://doi.org/10.1007/s10773-021-04775-3

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