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Article Dans Une Revue J.Phys.A Année : 2024

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

Résumé

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.

Dates et versions

hal-04170750 , version 1 (25-07-2023)

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Hamza Jaffali, Frédéric Holweck, Luke Oeding. Maximally entangled real states and SLOCC invariants: the 3-qutrit case. J.Phys.A, 2024, 57 (14), pp.145301. ⟨10.1088/1751-8121/ad3193⟩. ⟨hal-04170750⟩
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