Maximally entangled real states and SLOCC invariants: the 3-qutrit case

• URL: http://arxiv.org/abs/2307.00970v1
• Date: Mon, 3 Jul 2023 12:41:30 GMT
• Title: Maximally entangled real states and SLOCC invariants: the 3-qutrit case
• Abstract summary: We study the case of real 3-qutrit systems and discover a new set of maximally entangled states. It is notable that the Aharonov state is a simultaneous maximizer for all 3 fundamental invariants. We show how to evaluate these invariants on any 3-qutrit state using basic matrix operations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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