Maximally entangled real states and SLOCC invariants: the 3-qutrit case
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917017102057472 |
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| author | Jaffali, Hamza Holweck, Frédéric Oeding, Luke |
| author_facet | Jaffali, Hamza Holweck, Frédéric Oeding, Luke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_00970 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Maximally entangled real states and SLOCC invariants: the 3-qutrit case Jaffali, Hamza Holweck, Frédéric Oeding, Luke Quantum Physics Algebraic Geometry Representation Theory 81P42, 81P45, 14N07, 15A69, 15A72 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. |
| title | Maximally entangled real states and SLOCC invariants: the 3-qutrit case |
| topic | Quantum Physics Algebraic Geometry Representation Theory 81P42, 81P45, 14N07, 15A69, 15A72 |
| url | https://arxiv.org/abs/2307.00970 |