Coxeter groups A4, B4 and D4 for two-qubit systems

Ramazan Koç, M. Yakup Haciibrahimoǧlu, Mehmet Koca

Research output: Contribution to journalArticle

Abstract

The Coxeter-Weyl groups W(A4), W(B4) and W(D 4) have proven very useful for two-qubit systems in quantum information theory. A simple technique is employed to construct the unitary matrix representations of the groups, based on quaternionic transformation of the usual reflection matrices. The von Neumann entropy of each reduced density matrix is calculated. It is shown that these unitary matrix representations are naturally related to various universal quantum gates and they lead to entangled states. Canonical decomposition of generators in terms of fundamental gate representations is given to construct the quantum circuits.

Original languageEnglish
Pages (from-to)247-260
Number of pages14
JournalPramana - Journal of Physics
Volume81
Issue number2
DOIs
Publication statusPublished - Aug 2013

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information theory
generators
entropy
decomposition

Keywords

  • Group theory in quantum mechanics
  • Quantum computation
  • Quantum information

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Coxeter groups A4, B4 and D4 for two-qubit systems. / Koç, Ramazan; Haciibrahimoǧlu, M. Yakup; Koca, Mehmet.

In: Pramana - Journal of Physics, Vol. 81, No. 2, 08.2013, p. 247-260.

Research output: Contribution to journalArticle

Koç, R, Haciibrahimoǧlu, MY & Koca, M 2013, 'Coxeter groups A4, B4 and D4 for two-qubit systems', Pramana - Journal of Physics, vol. 81, no. 2, pp. 247-260. https://doi.org/10.1007/s12043-013-0570-z
Koç, Ramazan ; Haciibrahimoǧlu, M. Yakup ; Koca, Mehmet. / Coxeter groups A4, B4 and D4 for two-qubit systems. In: Pramana - Journal of Physics. 2013 ; Vol. 81, No. 2. pp. 247-260.
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