 
Summary: Generalized KochenSpecker 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 KochenSpecker 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 KochenSpecker, KochenSpecker, 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 KochenSpecker 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
