Foundations of Physics Letters

, Volume 13, Issue 6, pp 499–519 | Cite as

HOW REYE'S CONFIGURATION HELPS IN PROVING THE BELL–KOCHEN–SPECKER THEOREM: A CURIOUS GEOMETRICAL TALE

  • P. K. Aravind
Article

Abstract

It is shown that the 24 quantum states or “rays” used by Peres (J. Phys. A24, 174-8 (1991)) to give a proof of the Bell–Kochen–Specker (BKS) theorem have a close connection with Reye's configuration, a system of twelve points and sixteen lines known to projective geometers for over a century. The interest of this observation stems from the fact that it provides a ready explanation for many of the regularities exhibited by the Peres rays and also permits a systematic construction of all possible non-coloring proofs of the BKS theorem based on these rays. An elementary exposition of the connection between the Peres rays and Reye's configuration is given, following which its applications to the BKS theorem are discussed.

Bell–Kochen–Specker theorem Reye's configuration 

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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • P. K. Aravind
    • 1
  1. 1.Department of PhysicsWorcester Polytechnic InstituteWorcester

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