The moduli space of three qutrit states

Details The moduli space of three qutrit states The moduli space of three qutrit states

2003-06-18

arxiv.org/abs/quant-ph/0306122v4

Physics

Quantum Physics

19 pages, revtex4, three figures; revised version

Scientific paper

10.1063/1.1809255

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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