Clifford group dipoles and the enactment of Weyl/Coxeter group W(E8) by entangling gates

Details Clifford group dipoles and the enactment of Weyl/Coxeter group W(E8) by entangling gates Clifford group dipoles and the enactment of Weyl/Coxeter group W(E8) by entangling gates

2009-04-23

arxiv.org/abs/0904.3691v4

General Mathematics Notes 2, 1 (2011) 96-113

Physics

Quantum Physics

version revised according the recommendations of a referee

Scientific paper

Peres/Mermin arguments about no-hidden variables in quantum mechanics are used for displaying a pair (R, S) of entangling Clifford quantum gates, acting on two qubits. From them, a natural unitary representation of Coxeter/Weyl groups W(D5) and W(F4) emerges, which is also reflected into the splitting of the n-qubit Clifford group Cn into dipoles C$\pm$n . The union of the three-qubit real Clifford group C+ 3 and the Toffoli gate ensures a orthogonal representation of the Weyl/Coxeter group W(E8), and of its relatives. Other concepts involved are complex reflection groups, BN pairs, unitary group designs and entangled states of the GHZ family.

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