QUANTUM STATES ARISING FROM THE PAULI GROUPS, SYMMETRIES AND PARADOXES

Michel R. P. Planat (1)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

We investigate multiple qubit Pauli groups and the quantum states/rays arising from their maximal bases. Remarkably, the real rays are carried by a Barnes-Wall lattice $BW_n$ ($n=2^m$). We focus on the smallest subsets of rays allowing a state proof of the Bell-Kochen-Specker theorem (BKS). BKS theorem rules out realistic {\it non-contextual} theories by resorting to impossible assignments of rays among a selected set of maximal orthogonal bases. We investigate the geometrical structure of small BKS-proofs $v-l$ involving $v$ rays and $l$ $2n$-dimensional bases of $n$-qubits. Specifically, we look at the classes of parity proofs $18-9$ with two qubits (A. Cabello, 1996), $36-11$ with three qubits (M. Kernaghan \& A. Peres, 1995) and related classes. One finds characteristic signatures of the distances among the bases, that carry various symmetries in their graphs.

Mots clés: multiple qubits; Barnes-Wall lattices; Bell-Kochen-Specker theorem.; Bell-Kochen-Specker theorem

Domaines: Physique Quantique [quant-ph]; Théorie des groupes [math.GR]

Michel R. P. Planat. QUANTUM STATES ARISING FROM THE PAULI GROUPS, SYMMETRIES AND PARADOXES. The XXIXth International Colloquium on Group-Theoretical Methods in Physics, Aug 2012, China. ⟨hal-00734602⟩