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

TL;DR

This paper investigates maximally entangled states in real 3-qutrit systems through polynomial SLOCC invariants, identifying new maximizers and analyzing their properties with computational methods.

Contribution

It introduces new maximally entangled states for real 3-qutrits, explores invariants' maximization, and provides methods to evaluate these invariants efficiently.

Findings

Aharonov state maximizes all three fundamental invariants.

Identified states that maximize the hyperdeterminant.

Analyzed invariants' behavior on random states.

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.