Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Zeitschrift für Naturforschung A

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

Willi-Hans Steeb, Yorick Hardy

Published Nov 1, 2011• 2 citations
Publisher

Abstract

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.

DOI
10.5560/zna.2011-0025

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.

Open Physics•May 16, 2009•2 citations

Entanglement, Disentanglement and Wigner Functions

Yorick Hardy, Willi-Hans Steeb, Ruedi Stoop

Entangled quantum states are an important component of quantum computing techniques such as quantum error-correction, dense coding and quantum teleportation. We describe how to generate fully entangled states in the Hilbert space C N ⊗ C N starting from a unitary matrix and show that they form an orthonormal basis in this space. Disentanglement is also discussed. Moreover we also calculate the Wigner function of fully entangled states.

Physica Scripta•Jan 1, 2004•1 citation

Diabolic points and entanglement

Willi-Hans Steeb

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

Physica Scripta•Feb 1, 2010•2 citations

A SEQUENCE OF QUANTUM GATES

Yorick Hardy, W.‐H. Steeb

We study a sequence of quantum gates in finite-dimensional Hilbert spaces given by the normalized eigenvectors of the unitary operators. The corresponding sequence of the Hamilton operators is also given. From the Hamilton operators we construct another hierarchy of quantum gates via the Cayley transform.

arXiv:1202.2259•International Journal of Geometric Methods in Modern Physics•Jul 26, 2012•2 citations

UNITARY OPERATORS, ENTANGLEMENT, AND GRAM–SCHMIDT ORTHOGONALIZATION

Yorick Hardy, Willi-Hans Steeb

We consider finite-dimensional Hilbert spaces [Formula: see text] with [Formula: see text] with n ≥ 2 and unitary operators. In particular, we consider the case n = 2m, where m ≥ 2 in order to study entanglement of states in these Hilbert spaces. Two normalized states ψ and ϕ in these Hilbert spaces [Formula: see text] are connected by a unitary transformation (n×n unitary matrices), i.e. ψ = Uϕ, where U is a unitary operator UU* = I. Given the normalized states ψ and ϕ, we provide an algorithm to find this unitary operator U for finite-dimensional Hilbert spaces. The construction is based on a modified Gram–Schmidt orthonormalization technique. A number of applications important in quantum computing are given. Symbolic C++ is used to give a computer algebra implementation in C++.

International Journal of Modern Physics C•Jun 1, 2009•0 citations

Spin Hamilton Operators, Symmetry Breaking, Energy Level Crossing, and Entanglement

Willi-Hans Steeb, Yorick Hardy, Jacqueline de Greef

We study finite-dimensional product Hilbert spaces, coupled spin systems, entanglement, and energy level crossing. The Hamilton operators are based on the Pauli group.We show that swapping the interacting term can lead from unentangled eigenstates to entangled eigenstates and from an energy spectrum with energy level crossing to avoided energy level crossing.

arXiv:1110.4204•Zeitschrift für Naturforschung A•Aug 20, 2012•1 citation
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.
Abstract We consider a hierarchy of Hamilton operators Ĥ N in finite dimensional Hilbert spaces C2N \mathbb{C}^{2^N } C2N. 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.
We consider finite-dimensional Hilbert spaces [Formula: see text] with [Formula: see text] with n ≥ 2 and unitary operators. In particular, we consider the case n = 2m, where m ≥ 2 in order to study entanglement of states in these Hilbert spaces. Two normalized states ψ and ϕ in these Hilbert spaces [Formula: see text] are connected by a unitary transformation (n×n unitary matrices), i.e. ψ = Uϕ, where U is a unitary operator UU* = I. Given the normalized states ψ and ϕ, we provide an algorithm to find this unitary operator U for finite-dimensional Hilbert spaces. The construction is based on a modified Gram–Schmidt orthonormalization technique. A number of applications important in quantum computing are given. Symbolic C++ is used to give a computer algebra implementation in C++.