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 three-dimensional
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.Comment: 5 pages, 1 figure; Version 2 - slightly expanded, accepted in Quantum
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