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arXiv · 2204.09586

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

K. Anjali·I. Reena·Sudha·B. G. Divyamani·H. S. Karthik·K. S. Mallesh·A. R. Usha Devi
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Abstract

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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K. Anjali, I. Reena, Sudha, B. G. Divyamani, H. S. Karthik, K. S. Mallesh, A. R. Usha Devi. 2022-04-20. Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states. https://arxiv.org/abs/2204.09586

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