167 research outputs found
Singularity of type arising from four qubit systems
An intriguing correspondence between four-qubit systems and simple
singularity of type is established. We first consider an algebraic
variety of separable states within the projective Hilbert space
. Then, cutting with a specific
hyperplane , we prove that the -hypersurface, defined from the section
, has an isolated singularity of type ; it is also shown
that this is the "worst-possible" isolated singularity one can obtain by this
construction. Moreover, it is demonstrated that this correspondence admits a
dual version by proving that the equation of the dual variety of , which is
nothing but the Cayley hyperdeterminant of type ,
can be expressed in terms of the SLOCC invariant polynomials as the
discriminant of the miniversal deformation of the -singularity.Comment: 20 pages, 5 table
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