Naimark dilation theorem

E924210

mathematical theorem theorem in functional analysis theorem in operator theory theorem in quantum measurement theory

The Naimark dilation theorem is a fundamental result in operator theory and quantum measurement theory stating that every positive operator-valued measure can be realized as the compression of a projection-valued measure on a larger Hilbert space.

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Observed surface forms (1)

Surface form	Occurrences
Naimark dilation	1

Statements (42)

Predicate	Object
instanceOf	mathematical theorem ⓘ theorem in functional analysis ⓘ theorem in operator theory ⓘ theorem in quantum measurement theory ⓘ
alsoKnownAs	Naimark dilation NERFINISHED ⓘ Naimark’s theorem NERFINISHED ⓘ
appliesTo	bounded operator-valued measures ⓘ countably additive POVMs ⓘ
concerns	Hilbert spaces NERFINISHED ⓘ dilations of operators ⓘ positive operator-valued measures ⓘ projection-valued measures ⓘ quantum measurements ⓘ
domain	complex Hilbert spaces ⓘ separable Hilbert spaces ⓘ
field	functional analysis ⓘ operator theory ⓘ quantum information theory ⓘ quantum measurement theory ⓘ
generalizes	representation of positive operator-valued measures by projections ⓘ
guaranteesExistenceOf	larger Hilbert space and PVM realizing a given POVM ⓘ
hasConsequence	implementation of POVMs as projective measurements on extended Hilbert spaces ⓘ realization of generalized measurements via ancilla systems ⓘ structure theory of quantum measurements ⓘ
historicalPeriod	20th century mathematics ⓘ
implies	every POVM is a compression of a PVM on a larger Hilbert space ⓘ every positive operator-valued measure admits a dilation to a projection-valued measure ⓘ generalized quantum measurements can be realized as projective measurements on an extended system ⓘ
namedAfter	Mark Naimark NERFINISHED ⓘ
relatedTo	POVM NERFINISHED ⓘ PVM ⓘ Stinespring dilation theorem NERFINISHED ⓘ quantum instruments ⓘ spectral theorem NERFINISHED ⓘ
typicalFormulation	for any POVM on a Hilbert space H there exists a Hilbert space K containing H and a PVM on K whose compression to H equals the POVM ⓘ
usedIn	C*-algebra theory ⓘ Stinespring dilation theorem proofs ⓘ operator algebras ⓘ quantum computing ⓘ quantum information theory ⓘ quantum measurement design ⓘ quantum state discrimination ⓘ

Referenced by (3)

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Mark Naimark → notableFor → Naimark dilation theorem ⓘ

Mark Naimark → hasTheoremNamedAfter → Naimark dilation theorem ⓘ

Mark Naimark → notableConcept → Naimark dilation theorem ⓘ

this entity surface form: Naimark dilation