Mermin's Pentagram as an Ovoid of PG(3,2) - Archive ouverte HAL Access content directly
Journal Articles EPL - Europhysics Letters Year : 2012

Mermin's Pentagram as an Ovoid of PG(3,2)

Abstract

Mermin's pentagram, a specific set of ten three-qubit observables arranged in quadruples of pairwise commuting ones into five edges of a pentagram and used to provide a very simple proof of the Kochen-Specker theorem, is shown to be isomorphic to an ovoid (elliptic quadric) of the three-dimensional projective space of order two, PG(3,2). This demonstration employs properties of the real three-qubit Pauli group embodied in the geometry of the symplectic polar space W(5,2) and rests on the facts that: 1) the four observables/operators on any of the five edges of the pentagram can be viewed as points of an affine plane of order two, 2) all the ten observables lie on a hyperbolic quadric of the five-dimensional projective space of order two, PG(5,2), and 3) that the points of this quadric are in a well-known bijective correspondence with the lines of PG(3,2).
Fichier principal
Vignette du fichier
mermin_pentagram.pdf (76.08 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00644786 , version 1 (25-11-2011)

Identifiers

Cite

Metod Saniga, Peter Levay. Mermin's Pentagram as an Ovoid of PG(3,2). EPL - Europhysics Letters, 2012, pp.50006. ⟨10.1209/0295-5075/97/50006⟩. ⟨hal-00644786⟩

Collections

INSMI TDS-MACS
184 View
223 Download

Altmetric

Share

Gmail Facebook X LinkedIn More