Publications in Scientific Journals:
A. Abbott, C.S. Calude, K. Svozil:
"A variant of the Kochen-Specker theorem localising value indefiniteness";
Journal of Mathematical Physics,
The Kochen-Specker theorem proves the inability to assign, simultaneously, noncontextual definite values to all (of a finite set of) quantum mechanical observables in a consistent manner. If one assumes that any definite values behave noncontextually, one can nonetheless only conclude that some observables (in this set) are value indefinite. In this paper, we prove a variant of the Kochen-Specker theorem showing that, under the same assumption of noncontextuality, if a single one-dimensional projection observable is assigned the definite value 1, then no one-dimensional projection observable that is incompatible (i.e., non-commuting) with this one can be assigned consistently a definite value. Unlike standard proofs of the Kochen-Specker theorem, in order to localise and show the extent of value indefiniteness,
this result requires a constructive method of reduction between Kochen-Specker sets. If a system is prepared in a pure state, then it is reasonable to assume that any value assignment (i.e., hidden variable model) for this system assigns the value 1 to the observable projecting onto the one-dimensional linear subspace
spanned by the corresponding vector, and the value 0 to those projecting onto linear subspaces orthogonal to it. Our result can be interpreted, under this assumption, as showing that the
outcome of a measurement of any other incompatible one-dimensional projection observable cannot be determined in advance, thus formalising a notion of quantum randomness.
In dieser Arbeit wird gezeigt, dass, relativ zu Standardannahmen in der Quantenphysik, alle Observable bis auf eine einzige (und deren Komplement) keinen "definierten" Wert vor ihrer Messung haben. Konsequenzen für die Konstruktion von Quanten-Zufallsgeneratoren werden erörtert.
quantum value indefiniteness, Kochen Specker Theorem, Zufallszahlengenerator
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
Created from the Publication Database of the Vienna University of Technology.