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Generalized Kochen-Specker theorem P. K. Aravind

Summary: Generalized Kochen-Specker theorem
P. K. Aravind
Physics Department, Worcester Polytechnic Institute, Worcester, Massachusetts 01609, USA
Received 10 June 2003; published 17 November 2003
A proof of the generalized Kochen-Specker theorem in two dimensions due to Cabello and Nakamura A.
Cabello, Phys. Rev. Lett. 90, 190401 2003 is extended to all higher dimensions. A set of 18 states in four
dimensions is used to give closely related proofs of the generalized Kochen-Specker, Kochen-Specker, and
Bell theorems that shed some light on the relationship between these three theorems.
DOI: 10.1103/PhysRevA.68.052104 PACS number s : 03.65.Ta
Cabello and Nakamura 1 recently proved a generaliza-
tion of the Kochen-Specker KS theorem 2 in two dimen-
sions suggested by a similar generalization of Gleason's
theorem 3 . The key element in the generalization of both
theorems is the replacement of von Neumann or projective
measurements by more general measurements described by
positive operator valued measures POVMs . This shift leads
to two unexpected, but pleasing, effects: it causes the validity
of both theorems to extend down to dimension 2 rather than
3 as previously , and it also makes the proofs of both theo-
rems much easier. The purpose of this paper is, first, to show


Source: Aravind, Padmanabhan K. - Department of Physics, Worcester Polytechnic Institute


Collections: Physics