2023/07/03 by Hamza Jaffali, Jaffali, Hamza, Frédéric Holweck +3 · 1 citation
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Computing Algorithms and Architecture #Quantum many-body systems
paper · doi:10.48550/arxiv.2307.00970
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.