### Abstract

The Coxeter-Weyl groups W(A_{4}), W(B_{4}) 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 language | English |
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Pages (from-to) | 247-260 |

Number of pages | 14 |

Journal | Pramana - Journal of Physics |

Volume | 81 |

Issue number | 2 |

DOIs | |

Publication status | Published - Aug 2013 |

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### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Pramana - Journal of Physics*,

*81*(2), 247-260. https://doi.org/10.1007/s12043-013-0570-z

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

Research output: Contribution to journal › Article

*Pramana - Journal of Physics*, vol. 81, no. 2, pp. 247-260. https://doi.org/10.1007/s12043-013-0570-z

}

TY - JOUR

T1 - Coxeter groups A4, B4 and D4 for two-qubit systems

AU - Koç, Ramazan

AU - Haciibrahimoǧlu, M. Yakup

AU - Koca, Mehmet

PY - 2013/8

Y1 - 2013/8

N2 - 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.

AB - 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.

KW - Group theory in quantum mechanics

KW - Quantum computation

KW - Quantum information

UR - http://www.scopus.com/inward/record.url?scp=84882768100&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84882768100&partnerID=8YFLogxK

U2 - 10.1007/s12043-013-0570-z

DO - 10.1007/s12043-013-0570-z

M3 - Article

VL - 81

SP - 247

EP - 260

JO - Pramana - Journal of Physics

JF - Pramana - Journal of Physics

SN - 0304-4289

IS - 2

ER -