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Article Dans Une Revue General Mathematics Notes Année : 2011

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

Résumé

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±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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Dates et versions

hal-00378095 , version 1 (23-04-2009)
hal-00378095 , version 2 (05-05-2009)
hal-00378095 , version 3 (18-09-2009)
hal-00378095 , version 4 (29-09-2009)

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Citer

Michel Planat. Clifford group dipoles and the enactment of Weyl/Coxeter group W(E8) by entangling gates. General Mathematics Notes, 2011, 2 (1), pp.96-113. ⟨hal-00378095v4⟩
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