Coxeter groups $A_{4}$, $B_{4}$ and $D_{4}$ for two-qubit systems

Pramana

M Yakup HaciibrahimoÄŸlu¹  Mehmet Koca2²  Ramazan Koç¹ 

[1] Department of Physics, Faculty of Engineering, University of Gaziantep, 27310 Gaziantep, Turkey$$;Department of Physics, College of Science, Sultan Qaboos University, P.O. Box 36, Al-Khoud 123, Muscat, Oman$$

关键词: Quantum computation;    quantum information;    group theory in quantum mechanics.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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.

【 授权许可】

Unknown