Finite geometry behind the Harvey-Chryssanthacopoulos four-qubit magic rectangle (pp1011-1016)
          Metod Saniga and Michel Planat
          doi: https://doi.org/10.26421/QIC12.11-12-8
Abstracts: A “magic rectangle” of eleven observables of four qubits, employed by Harvey and Chryssanthacopoulos (2008) to prove the Bell-Kochen-Specker theorem in a 16-dimensional Hilbert space, is given a neat finite-geometrical reinterpretation in terms of the structure of the symplectic polar space W(7, 2) of the real four-qubit Pauli group. Each of the four sets of observables of cardinality five represents an elliptic quadric in the threedimensional projective space of order two (PG(3, 2)) it spans, whereas the remaining set of cardinality four corresponds to an affine plane of order two. The four ambient PG(3, 2)s of the quadrics intersect pairwise in a line, the resulting six lines meeting in a point. Projecting the whole configuration from this distinguished point (observable) one gets another, complementary “magic rectangle” of the same qualitative structure.
Key words:  Bell-Kochen-Specker Theorem, “Magic Rectangle” of Observables, FourQubit Pauli Group, Finite Geometry