6533b82bfe1ef96bd128e15e
RESEARCH PRODUCT
Three-qutrit entanglement and simple singularities
Frédéric HolweckHamza Jaffalisubject
Statistics and ProbabilityMathematics::Functional AnalysisQuantum PhysicsPure mathematicsSingularity theory010102 general mathematicsGeneral Physics and AstronomyStatistical and Nonlinear PhysicsAlgebraic varietyQuantum PhysicsQuantum entanglementSingular point of a curve01 natural sciencesMathematics - Algebraic GeometryHypersurfaceHyperplaneModeling and Simulation0103 physical sciencesProjective Hilbert space0101 mathematicsQutrit010306 general physicsMathematical PhysicsMathematicsdescription
In this paper, we use singularity theory to study the entanglement nature of pure three-qutrit systems. We first consider the algebraic variety $X$ of separable three-qutrit states within the projective Hilbert space $\mathbb{P}(\mathcal{H}) = \mathbb{P}^{26}$. Given a quantum pure state $|\varphi\rangle\in \mathbb{P}(\mathcal{H})$ we define the $X_\varphi$-hypersuface by cutting $X$ with a hyperplane $H_\varphi$ defined by the linear form $\langle\varphi|$ (the $X_\varphi$-hypersurface of $X$ is $X\cap H_\varphi \subset X$). We prove that when $|\varphi\rangle$ ranges over the SLOCC entanglement classes, the "worst" possible singular $X_\varphi$-hypersuface with isolated singularities, has a unique singular point of type $D_4$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-06-17 | Journal of Physics A: Mathematical and Theoretical |