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2009 | 7 | 4 | 854-859

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A hierarchy of Hamilton operators and entanglement


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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
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.


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


  • [1] J. A. Cronin, D. F. Greenberg, V. L. Telegdi, University of Chicago Graduate Problems in Physics (Addison-Wesley, Reading, Massachusetts, 1967)
  • [2] A. Zrenner et al., Nature 418, 612 (2002) http://dx.doi.org/10.1038/nature00912[Crossref]
  • [3] R. Deblock, E. Onac, L. Gurevich, L. P. Kouwenhoven, Science 301, 203 (2003) http://dx.doi.org/10.1126/science.1084175[Crossref]
  • [4] A. Shnirman, D. Mozyrsky, I. Martin, Europhys. Lett. 67, 840 (2004) http://dx.doi.org/10.1209/epl/i2003-10309-6[Crossref]
  • [5] S. Ashhab, J. R. Johansson, F. Nori, New J. Phys. 8, 103 (2006) http://dx.doi.org/10.1088/1367-2630/8/6/103[Crossref]
  • [6] L. Faoro, L. Ioffe, Phys. Rev. Lett. 96, 04001 (2006) http://dx.doi.org/10.1103/PhysRevLett.96.047001[Crossref]
  • [7] A. M. Zagoskin, S. Ashhab, J. R. Johansson, F. Nori, Phys. Rev. Lett. 97, 077001 (2006) http://dx.doi.org/10.1103/PhysRevLett.97.077001[Crossref]
  • [8] R. M. Angelo, W. F. Wreszinski, Ann. Phys.-New York 322, 769 (2007) http://dx.doi.org/10.1016/j.aop.2007.01.001[Crossref]
  • [9] A. Pechen, D. Prokhorenko, R. Wu, H. Rabitz, Journal of Physics A: Mathematical and Theoretical 41, 045205 (2008) http://dx.doi.org/10.1088/1751-8113/41/4/045205[Crossref]
  • [10] M. A. Nielsen, I. L. Chuang, Quantum Computing and Quantum Information (Cambridge University Press, 2000)
  • [11] W.-H. Steeb, Y. Hardy, Problems and Solutions in Quantum Computing and Quantum Information, second edition (World Scientific, Singapore, 2006)
  • [12] W.-H. Steeb, Matrix Calculus and Kronecker Product with Applications and C++ Programs (World Scientific, Singpore, 1997)
  • [13] W.-H. Steeb, Problems and Solutions in Introductory and Advanced Matrix Calculus (World Scientific, Singapore, 2006)
  • [14] V. Coffman, J. Kundu, W. K. Wootters, Phys. Rev. A 61, 052306 (2000) http://dx.doi.org/10.1103/PhysRevA.61.052306[Crossref]
  • [15] A. Wong, N. Christensen, Phys. Rev. A 63 044301 (2001) http://dx.doi.org/10.1103/PhysRevA.63.044301
  • [16] F. Hund, Z. Phys. 40, 742 (1927) http://dx.doi.org/10.1007/BF01400234[Crossref]
  • [17] J. von Neumann, E. Wigner, Phys. Z. 30, 467 (1929)
  • [18] W.-H. Steeb, Problems and Solutions in Theoretical and Mathematical Physics, second edition, Volume II: Advanced Level (World Scientific, Singapore, 2003)
  • [19] W.-H. Steeb, A. J. van Tonder, C. M. Villet, S. J. M. Brits, Found. Phys Lett 1, 147 (1988) http://dx.doi.org/10.1007/BF00661855[Crossref]

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