A hierarchy of Hamilton operators and entanglement

• Authors: Willi-Hans Steeb , Yorick Hardy
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

entanglement; energy level crossing; eigenvalue problem

Discipline

• 03.65.Ud: Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)(for entanglement production and manipulation, see 03.67.Bg; for entanglement measures, witnesses etc., see 03.67.Mn; for entanglement in Bose-Einstein condensates, see 03.75.Gg)

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2009
• Volume: 7
• Issue: 4
• Pages: 854-859

Dates

published

1 - 12 - 2009

online

21 - 7 - 2009

Contributors

author

Willi-Hans Steeb

• International School for Scientific Computing, University of Johannesburg, Auckland Park, 2006, South Africa

author

Yorick Hardy

• International School for Scientific Computing, University of Johannesburg, Auckland Park, 2006, South Africa

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Identifiers

DOI

10.2478/s11534-009-0075-z