dorsal/arxiv
View SchemaThe moduli space of three qutrit states
| Authors | E. Briand, J. -G. Luque, J. -Y. Thibon, F. Verstraete |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306122 |
| URL | https://arxiv.org/abs/quant-ph/0306122 |
| DOI | 10.1063/1.1809255 |
| Journal | J. Math. Phys. 45 (2004), 4855-4867 |
Abstract
We study the invariant theory of trilinear forms over a three-dimensional complex vector space, and apply it to investigate the behaviour of pure entangled three-partite qutrit states and their normal forms under local filtering operations (SLOCC). We describe the orbit space of the SLOCC group $SL(3,\C)^{\times 3}$ both in its affine and projective versions in terms of a very symmetric normal form parameterized by three complex numbers. The parameters of the possible normal forms of a given state are roots of an algebraic equation, which is proved to be solvable by radicals. The structure of the sets of equivalent normal forms is related to the geometry of certain regular complex polytopes.
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"abstract": "We study the invariant theory of trilinear forms over a three-dimensional\ncomplex vector space, and apply it to investigate the behaviour of pure\nentangled three-partite qutrit states and their normal forms under local\nfiltering operations (SLOCC). We describe the orbit space of the SLOCC group\n$SL(3,\\C)^{\\times 3}$ both in its affine and projective versions in terms of a\nvery symmetric normal form parameterized by three complex numbers. The\nparameters of the possible normal forms of a given state are roots of an\nalgebraic equation, which is proved to be solvable by radicals. The structure\nof the sets of equivalent normal forms is related to the geometry of certain\nregular complex polytopes.",
"arxiv_id": "quant-ph/0306122",
"authors": [
"E. Briand",
"J. -G. Luque",
"J. -Y. Thibon",
"F. Verstraete"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1809255",
"journal_ref": "J. Math. Phys. 45 (2004), 4855-4867",
"title": "The moduli space of three qutrit states",
"url": "https://arxiv.org/abs/quant-ph/0306122"
},
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