Geometric contextuality from the Maclachlan-Martin Kleinian groups
نویسنده
چکیده
There are contextual sets of multiple qubits whose commutation is parametrized thanks to the coset geometry G of a subgroup H of the two-generator free group G = 〈x, y〉. One defines geometric contextuality from the discrepancy between the commutativity of cosets on G and that of quantum observables. It is shown in this paper that Kleinian subgroups K = 〈f, g〉 that are non-compact, arithmetic, and generated by two elliptic isometries f and g (the Martin-Maclachlan classification), are appropriate contextuality filters. Standard contextual geometries such as some thin generalized polygons (starting with Mermin’s 3 × 3 grid) belong to this frame. The Bianchi groups PSL(2, Od), d ∈ {1, 3} defined over the imaginary quadratic field Od = Q( √ −d) play a special role.
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