Kochen–Specker theorem

E645528

no-go theorem result in quantum foundations theorem in quantum mechanics

The Kochen–Specker theorem is a foundational result in quantum mechanics showing that it is impossible to assign consistent, noncontextual definite values to all quantum observables, thereby ruling out a broad class of hidden-variable theories.

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Observed surface forms (2)

Surface form	Occurrences
Peres–Kochen–Specker theorem formulation	1
Peres–Mermin magic square	1

Statements (49)

Predicate	Object
instanceOf	no-go theorem ⓘ result in quantum foundations ⓘ theorem in quantum mechanics ⓘ
appliesTo	Hilbert spaces of dimension at least three ⓘ
assumes	functional composition principle for value assignments ⓘ noncontextuality of hidden variables ⓘ
citation	S. Kochen and E. P. Specker, Journal of Mathematics and Mechanics 17, 59–87 (1967) NERFINISHED ⓘ
concerns	contextuality ⓘ hidden-variable theories ⓘ projection operators on Hilbert space ⓘ quantum observables ⓘ value definiteness ⓘ
countryOfOrigin	Switzerland ⓘ
doesNotApplyTo	two-dimensional Hilbert spaces ⓘ
field	mathematical physics ⓘ philosophy of physics ⓘ quantum foundations ⓘ quantum logic ⓘ quantum mechanics ⓘ
hasConsequence	measurement outcomes in quantum mechanics cannot be explained by noncontextual hidden parameters ⓘ motivates experimental tests of quantum contextuality ⓘ no global assignment of predetermined outcomes to all measurements is compatible with quantum predictions ⓘ supports contextual interpretations of quantum theory ⓘ
hasVariant	finite-precision versions of the Kochen–Specker theorem ⓘ state-independent contextuality proofs ⓘ
implies	impossibility of assigning noncontextual definite values to all quantum observables ⓘ value assignments to observables must be contextual ⓘ
influenced	development of contextuality-based quantum information protocols ⓘ philosophical debates on realism in quantum mechanics ⓘ
isTypeOf	no-hidden-variables theorem NERFINISHED ⓘ
mainClaim	Noncontextual hidden-variable theories are incompatible with quantum mechanics in Hilbert spaces of dimension three or greater ⓘ
mathematicalFormulation	impossibility of a noncontextual 0–1 valuation on all projections preserving functional relations ⓘ
namedAfter	Ernst Specker NERFINISHED ⓘ Simon Kochen NERFINISHED ⓘ
originalTitle	The problem of hidden variables in quantum mechanics NERFINISHED ⓘ
publicationYear	1967 ⓘ
publishedIn	Journal of Mathematics and Mechanics NERFINISHED ⓘ
relatedTo	Bell's theorem NERFINISHED ⓘ Gleason's theorem NERFINISHED ⓘ contextuality in quantum mechanics ⓘ nonlocality ⓘ quantum logic no-go theorems ⓘ
rulesOut	global two-valued measures on the projection lattice of a Hilbert space of dimension at least three ⓘ noncontextual hidden-variable theories ⓘ
status	proven ⓘ
usesConcept	Boolean homomorphisms on projection lattices ⓘ lattice of projections of a Hilbert space ⓘ orthogonality of vectors ⓘ projection-valued measures ⓘ

Referenced by (5)

Full triples — surface form annotated when it differs from this entity's canonical label.

Ernst Specker → knownFor → Kochen–Specker theorem ⓘ

Ernst Specker → coAuthorOf → Kochen–Specker theorem ⓘ

Ernst Specker → notableWork → Kochen–Specker theorem ⓘ

Asher Peres → notableFor → Kochen–Specker theorem ⓘ

this entity surface form: Peres–Mermin magic square

Asher Peres → notableFor → Kochen–Specker theorem ⓘ

this entity surface form: Peres–Kochen–Specker theorem formulation