A Variant of the Kochen-Specker Theorem Localising Value Indefiniteness (Revision1)

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dc.contributor.author Abbott, AA en
dc.contributor.author Calude, CS en
dc.contributor.author Svozil, K en
dc.date.accessioned 2016-01-04T21:55:56Z en
dc.date.available 2016-01-04T21:55:56Z en
dc.date.issued 2015 en
dc.identifier.citation CDMTCS Research Reports CDMTCS-478 (2015) en
dc.identifier.issn 1178-3540 en
dc.identifier.uri http://hdl.handle.net/2292/27847 en
dc.description.abstract 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 |yi, 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 onedimensional linear subspace spanned by |yi, 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. en
dc.publisher Department of Computer Science, The University of Auckland, New Zealand en
dc.relation.ispartofseries CDMTCS Research Report Series en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.source.uri https://www.cs.auckland.ac.nz/research/groups/CDMTCS/researchreports/index.php en
dc.title A Variant of the Kochen-Specker Theorem Localising Value Indefiniteness (Revision1) en
dc.type Technical Report en
dc.subject.marsden Fields of Research en
dc.rights.holder The author(s) en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en

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