Maximally entangled real states and SLOCC invariants: the 3-qutrit case
Abstract
The absolute values of polynomial SLOCC invariants (which always vanish on separable states) can be seen as measures of entanglement. We study the case of real 3-qutrit systems and discover a new set of maximally entangled states (from the point of view of maximizing the hyperdeterminant). We also study the basic fundamental invariants and find real 3-qutrit states that maximize their absolute values. It is notable that the Aharonov state is a simultaneous maximizer for all 3 fundamental invariants. We also study the evaluation of these invariants on random real 3-qutrit systems and analyze their behavior using histograms and level-set plots. Finally, we show how to evaluate these invariants on any 3-qutrit state using basic matrix operations.
Keywords
Cite
@article{arxiv.2307.00970,
title = {Maximally entangled real states and SLOCC invariants: the 3-qutrit case},
author = {Hamza Jaffali and Frédéric Holweck and Luke Oeding},
journal= {arXiv preprint arXiv:2307.00970},
year = {2025}
}
Comments
20 pages, 6 figures, 2 ancillary files