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 |
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dc.date.available |
2016-01-04T21:55:56Z |
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dc.date.issued |
2015 |
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dc.identifier.citation |
CDMTCS Research Reports CDMTCS-478 (2015) |
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dc.identifier.issn |
1178-3540 |
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dc.identifier.uri |
http://hdl.handle.net/2292/27847 |
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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. |
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dc.publisher |
Department of Computer Science, The University of Auckland, New Zealand |
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dc.relation.ispartofseries |
CDMTCS Research Report Series |
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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. |
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dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
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dc.source.uri |
https://www.cs.auckland.ac.nz/research/groups/CDMTCS/researchreports/index.php |
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dc.title |
A Variant of the Kochen-Specker Theorem Localising Value Indefiniteness (Revision1) |
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dc.type |
Technical Report |
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dc.subject.marsden |
Fields of Research |
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dc.rights.holder |
The author(s) |
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dc.rights.accessrights |
http://purl.org/eprint/accessRights/OpenAccess |
en |