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Journal Articles Quantum Information & Computation Year : 2012

Finite Geometry Behind the Harvey-Chryssanthacopoulos Four-Qubit Magic Rectangle

Abstract

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.
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Dates and versions

hal-00692040 , version 1 (27-04-2012)

Identifiers

  • HAL Id : hal-00692040 , version 1

Cite

Metod Saniga, Michel Planat. Finite Geometry Behind the Harvey-Chryssanthacopoulos Four-Qubit Magic Rectangle. Quantum Information & Computation, 2012, 11, pp.1011-1016. ⟨hal-00692040⟩
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