Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states
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.
Keywords
Cite
@article{arxiv.2204.09586,
title = {Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states},
author = {K. Anjali and I. Reena and Sudha and B. G. Divyamani and H. S. Karthik and K. S. Mallesh and A. R. Usha Devi},
journal= {arXiv preprint arXiv:2204.09586},
year = {2022}
}
Comments
arXiv 2208.03024 is version 2 of 2204.09586 and by mistake it was uploaded as a new article