arXiv subjects

K. Anjali

Publications and source records attributed to K. Anjali.

3 recordsLinked to original sources

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.

quant-ph↗

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.

quant-ph↗

arXiv2021

Characterizing nonlocality of pure symmetric three-qubit states

We explore nonlocality of three-qubit pure symmetric states shared between Alice, Bob and Charlie using the Clauser-Horne-Shimony-Holt (CHSH) inequality. We make use of the elegant parametrization in the canonical form of these states, proposed by Meill and Meyer (Phys. Rev. A, 96, 062310 (2017)) based on Majorana geometric representation. The reduced two-qubit states, extracted from an arbitrary pure entangled symmetric three-qubit state do not violate the CHSH inequality and hence they are CHSH-local. However, when Alice and Bob perform a CHSH test, after conditioning over measurement results of Charlie, nonlocality of the state is revealed. We have also shown that two different families of three-qubit pure symmetric states, consisting of two and three distinct spinors (qubits) respectively, can be distinguished based on the strength of violation in the conditional CHSH nonlocality test. Furthermore, we identify six of the 46 classes of tight Bell inequalities in the three-party, two-setting, two-outcome i.e., (3,2,2) scenario (Phys. Rev. A 94, 062121 (2016)). Among the two inequivalent families of three-qubit pure symmetric states, only the states belonging to three distinct spinor class show maximum violations of these six tight Bell inequalities.

quant-ph↗