Abstract
Abstract
The absolute values of polynomial SLOCC invariants (which always vanish on separable states) can be seen as entanglement measures. 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 three 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.
Funder
Centre National de la Recherche Scientifique
Thomas Jefferson Foundation
Reference49 articles.
1. Étude de l’Intrication dans les Algorithmes Quantiques: approche Géométrique et Outils Dérivés;Jaffali,2020
2. Asymptotic improvements to quantum circuits via qutrits;Gokhale,2019
3. Three-qutrit entanglement and simple singularities;Holweck;J. Phys. A: Math. Theor.,2016
4. High-fidelity qutrit entangling gates for superconducting circuits;Goss;Nat. Commun.,2022
5. Fault-tolerant quantum computation with higher-dimensional systems;Gottesman;Chaos Solitons Fractals,1999