arXiv subjects

Seeta Vasudevrao

Publications and source records attributed to Seeta Vasudevrao.

2 recordsLinked to original sources

arXiv2022

Margenau-Hill operator valued measures and joint measurability

We employ the Margenau-Hill (MH) correspondence rule for associating classical functions with quantum operators to construct quasi-probability mass functions. Using this we obtain the fuzzy one parameter quasi measurement operator (QMO) characterizing the incompatibility of non-commuting spin observables of qubits, qutrits and 2-qubit systems. Positivity of the fuzzy MH-QMO places upper bounds on the associated unsharpness parameter. This serves as a sufficient condition for measurement incompatibility of spin observables. We assess the amount of unsharpness required for joint measurability (compatibility) of the non-commuting qubit, qutrit and 2-qubit observables. We show that the {\em degree of compatibility} of a pair of orthogonal qubit observables agrees perfectly with the necessary and sufficient conditions for joint measurability. Furthermore, we obtain analytical upper bounds on the unsharpness parameter specifying the range of joint measurability of spin components of qutrits and pairs of orthogonal spin observables of a 2-qubit system. Our results indicate that the measurement incompatibility of spin observables increases with Hilbert space dimension.

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arXiv2021

Sum Uncertainty Relations: Uncertainty Regions for Qubits and Qutrits

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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