Physica Scripta

Diabolic points and entanglement

Willi-Hans Steeb

Published Feb 1, 2010• 2 citations

Abstract

Diabolic points and entanglement for a hierarchy of spin Hamilton operators acting in the finite-dimensional Hilbert space are investigated.

DOI: 10.1088/0031-8949/81/02/025012

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A hierarchy of Hamilton operators and entanglement

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Abstract We consider a hierarchy of Hamilton operators Ĥ N in finite dimensional Hilbert spaces $$ \mathbb{C}^{2^N } $$. We show that the eigenstates of Ĥ N are fully entangled for N even. We also calculate the unitary operator U N(t) = exp(—Ĥ N t/ħ) for the time evolution and show that unentangled states can be transformed into entangled states using this operator. We also investigate energy level crossing for this hierarchy of Hamilton operators.

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Physica Scripta

Diabolic points and entanglement

Willi-Hans Steeb

Published Feb 1, 2010• 2 citations

Publisher

Abstract

Diabolic points and entanglement for a hierarchy of spin Hamilton operators acting in the finite-dimensional Hilbert space are investigated.

DOI: 10.1088/0031-8949/81/02/025012

Related papers

A hierarchy of Hamilton operators and entanglement

Willi-Hans Steeb, Yorick Hardy

Abstract We consider a hierarchy of Hamilton operators Ĥ N in finite dimensional Hilbert spaces $\mathbb{C}^{2^N }$ . We show that the eigenstates of Ĥ N are fully entangled for N even. We also calculate the unitary operator U N(t) = exp(—Ĥ N t/ħ) for the time evolution and show that unentangled states can be transformed into entangled states using this operator. We also investigate energy level crossing for this hierarchy of Hamilton operators.Abstract We consider a hierarchy of Hamilton operators Ĥ N in finite dimensional Hilbert spaces $$ \mathbb{C}^{2^N } $$. We show that the eigenstates of Ĥ N are fully entangled for N even. We also calculate the unitary operator U N(t) = exp(—Ĥ N t/ħ) for the time evolution and show that unentangled states can be transformed into entangled states using this operator. We also investigate energy level crossing for this hierarchy of Hamilton operators.

Open PhysicsMay 16, 20092 citations

Supersymmetric Hamilton Operator and Entanglement

Willi-Hans Steeb, Yorick Hardy

We study the entanglement of Fermi particles of a supersymmetric Hamilton operator given by a simple Fermi-Bose system

Zeitschrift für Naturforschung AApr 1, 20060 citations

N-tangle, Entangled Orthonormal Basis, and a Hierarchy of Spin Hamilton Operators

Willi-Hans Steeb, Yorick Hardy

An N-tangle can be defined for the finite dimensional Hilbert space H = C2N , with N = 3 or N even.We give an orthonormal basis which is fully entangled with respect to this measure.We provide a spin Hamilton operator which has this entangled basis as normalized eigenvectors if N is even. From these normalized entangled states a Bell matrix is constructed and the cosine-sine decomposition is calculated. If N is odd the normalized eigenvectors can be entangled or unentangled depending on the parameters.An N-tangle can be defined for the finite dimensional Hilbert space H = C2N , with N = 3 or N even.We give an orthonormal basis which is fully entangled with respect to this measure.We provide a spin Hamilton operator which has this entangled basis as normalized eigenvectors if N is even. From these normalized entangled states a Bell matrix is constructed and the cosine-sine decomposition is calculated. If N is odd the normalized eigenvectors can be entangled or unentangled depending on the parameters.

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Willi-Hans Steeb, Yorick Hardy

Jan 1, 20145 citations

Abstract We consider a hierarchy of Hamilton operators Ĥ N in finite dimensional Hilbert spaces

\mathbb{C}^{2^N }

. We show that the eigenstates of Ĥ N are fully entangled for N even. We also calculate the unitary operator U N(t) = exp(—Ĥ N t/ħ) for the time evolution and show that unentangled states can be transformed into entangled states using this operator. We also investigate energy level crossing for this hierarchy of Hamilton operators.