arXiv subjects

I. Reena

Publications and source records attributed to I. Reena.

5 recordsLinked to original sources

arXiv2022

Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states

The quantum steering ellipsoid inscribed inside the Bloch sphere offers an elegant geometric visualization of two-qubit states shared between Alice and Bob. The set of Bloch vectors of Bob's qubit, steered by Alice via all possible local measurements on her qubit, constitutes the steering ellipsoid. The steering ellipsoids are shown to be effective in capturing quantum correlation properties, such as monogamy, exhibited by entangled multiqubit systems. We focus here on the canonical ellipsoids of two-qubit states realized by incorporating optimal local filtering operations by Alice and Bob on their respective qubits. Based on these canonical forms we show that the reduced two-qubit states drawn from pure entangled three-qubit permutation symmetric states, which are inequivalent under stochastic local operations and classcial communication (SLOCC), carry distinct geometric signatures. We provide detailed analysis of the SLOCC canonical forms and the associated steering ellipsoids of the reduced two-qubit states extracted from entangled three-qubit pure symmetric states: We arrive at (i) a prolate spheroid centered at the origin of the Bloch sphere -- with longest semiaxis along the z-direction (symmetry axis of the spheroid) equal to 1 -- in the case of pure symmetric three-qubit states constructed by permutation of 3 distinct spinors and (ii) an oblate spheroid centered at $(0,0,1/2)$ inside the Bloch sphere, with fixed semiaxes lengths (1/Sqrt[2],\, 1/Sqrt[2],\, 1/2)), when the three-qubit pure state is constructed via symmetrization of 2 distinct spinors. We also explore volume monogamy relations formulated in terms of the volumes of the steering ellipsoids of the SLOCC inequivalent pure entangled three-qubit symmetric states.

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arXiv2022

Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states

We show that the pure entangled three-qubit symmetric states which are inequivalent under stochastic local operations and classcial communication (SLOCC) exhibit distinct geometric representation in terms of a spheroid inscribed within the Bloch sphere. We provide detailed analysis of the SLOCC canonical forms of the reduced two-qubit states extracted from entangled three-qubit pure symmetric states. Based on the Lorentz canonical forms of these states we arrive at two different geometrical representations: (i) a prolate spheroid centered at the origin of the Bloch sphere -- with longest semiaxis along the z-direction (symmetry axis of the spheroid) equal to 1 -- in the case of pure permutation symmetric three-qubit states constructed from 3 distinct spinors and (ii) a spheroid centered at (0,0,1/2) inside the Bloch sphere, with fixed semiaxes lengths (1/sqrt{2}, 1/sqrt{2}, 1/2) when the three-qubit pure state is constructed via symmetrization of 2 distinct spinors.

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arXiv2021

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

Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems

We show that violation of variance based local sum uncertainty relation (LSUR) for angular momentum operators of a bipartite system, proposed by Hofmann and Takeuchi~[Phys.Rev.A {\bf 68}, 032103 (2003)], reflects entanglement in the equal bipartitions of an $N$-qubit symmetric state with even qubits. We establish the one-to-one connection with the violation of LSUR with negativity of covariance matrix [Phys. Lett. A, {\bf 364}, 203 (2007)] of the two-qubit reduced system of a permutation symmetric $N$-qubit state.

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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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