Clifford group dipoles and the enactment of Weyl/Coxeter group W (E8) by entangling gates
نویسنده
چکیده
Peres/Mermin arguments about no-hidden variables in quantummechanics are used for displaying a pair (R,S) of entangling Clifford quantum gates, acting on two qubits. From them, a natural unitary realization 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 group dipoles C± n . The union of the three-qubit real Clifford group C 3 and the Toffoli gate ensures a orthogonal realization 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, W and chain families.
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