Physics:Quantum Projective measurement - Revision history

WikiHarold: Restore missing Quantum reference definitions

2026-05-24T00:31:25Z

Restore missing Quantum reference definitions

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	where <math>\rho</math> is the state of the system.<ref name=Nielsen/>		where <math>\rho</math> is the state of the system.<ref name=Nielsen>{{cite book \|last1=Nielsen \|first1=Michael A. \|last2=Chuang \|first2=Isaac L. \|title=Quantum Computation and Quantum Information \|publisher=Cambridge University Press \|year=2010}}</ref>

	After the measurement, the state collapses to		After the measurement, the state collapses to
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	This process is known as the '''projection postulate'''.<ref name=Neumann/>		This process is known as the '''projection postulate'''.<ref name=Neumann>{{cite book \|last=von Neumann \|first=John \|title=Mathematical Foundations of Quantum Mechanics \|year=1932}}</ref>

	== Physical interpretation ==		== Physical interpretation ==
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	== References ==		= References =
	{{reflist\|3}}		{{reflist\|3}}

	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}
	{{Sourceattribution\|Physics:Quantum Projective measurement\|1}}		{{Sourceattribution\|Physics:Quantum Projective measurement\|1}}

Maintenance script: Normalize quantum page header order

2026-05-22T11:32:33Z

Normalize quantum page header order

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	{{Quantum book backlink\|Measurement and information}}		{{Quantum book backlink\|Measurement and information}}
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Maintenance script: Clean Book label remnants and backlink spacing

2026-05-22T11:10:53Z

Clean Book label remnants and backlink spacing

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2026-05-22T11:03:05Z

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	{{Short description\|Quantum Collection topic on Quantum Projective measurement}}~~Book I~~		{{Short description\|Quantum Collection topic on Quantum Projective measurement}}

	{{Quantum book backlink\|Measurement and information}}		{{Quantum book backlink\|Measurement and information}}

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2026-05-22T10:48:07Z

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Maintenance script: Apply Quantum previous-next navigation

2026-05-20T12:24:54Z

Apply Quantum previous-next navigation

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	{{Quantum book backlink\|Measurement and information}}		{{Quantum book backlink\|Measurement and information}}
			{{Quantum article nav\|previous=Physics:Quantum Measurement operators\|previous label=Measurement operators\|next=Physics:Quantum POVM\|next label=POVM}}

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Maintenance script: Improve Book I intro quality

2026-05-20T09:03:57Z

Improve Book I intro quality

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	'''Projective measurement''' is a ~~Book I topic in the Quantum Collection. A~~ projective measurement (also called a von Neumann measurement) is a fundamental type of measurement in quantum mechanics in which the state of a system is projected onto an eigenstate of an observable. Projective measurements represent the simplest and most idealized form of quantum measurement and form the basis for more general frameworks such as positive operator-valued measurements (POVMs) and quantum instruments. A projective measurement (also called a von Neumann measurement) is a fundamental type of measurement in quantum mechanics in which the state of a system is projected onto an eigenstate of an observable. Projective measurements represent the simplest and most idealized form of quantum measurement and form the basis for more general frameworks such as positive operator-valued measurements (POVMs) and quantum instruments.		'''Projective measurement''' a projective measurement (also called a von Neumann measurement) is a fundamental type of measurement in quantum mechanics in which the state of a system is projected onto an eigenstate of an observable. Projective measurements represent the simplest and most idealized form of quantum measurement and form the basis for more general frameworks such as positive operator-valued measurements (POVMs) and quantum instruments. A projective measurement (also called a von Neumann measurement) is a fundamental type of measurement in quantum mechanics in which the state of a system is projected onto an eigenstate of an observable. Projective measurements represent the simplest and most idealized form of quantum measurement and form the basis for more general frameworks such as positive operator-valued measurements (POVMs) and quantum instruments. Let an observable be represented by a self-adjoint operator with spectral decomposition
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Maintenance script: Clean missing Book I links and template output

2026-05-20T08:47:21Z

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	Projective measurements are a special case of more general measurement frameworks:		Projective measurements are a special case of more general measurement frameworks:

	* A [[positive operator-valued measurement]] (POVM) generalizes projective measurements by allowing non-orthogonal measurement operators.<ref name=Nielsen/>		* A positive operator-valued measurement (POVM) generalizes projective measurements by allowing non-orthogonal measurement operators.<ref name=Nielsen/>
	* A '''quantum instrument''' provides a full description of a measurement, including both the classical outcome and the post-measurement quantum state.		* A '''quantum instrument''' provides a full description of a measurement, including both the classical outcome and the post-measurement quantum state.

Maintenance script: Clean Book I red links, intro, and image slots

2026-05-20T08:14:43Z

Clean Book I red links, intro, and image slots

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	A '''~~projective~~ measurement''' (also called a ~~'''~~von Neumann measurement~~'''~~) is a fundamental type of measurement in [[quantum mechanics]] in which the state of a system is projected onto an eigenstate of an observable.~~<ref name=Neumann>{{cite book \|last=~~von Neumann ~~\|first=John \|title=Mathematical Foundations~~ of ~~Quantum Mechanics \|year=1932}}</ref>~~		'''Projective measurement''' is a Book I topic in the Quantum Collection. A projective measurement (also called a von Neumann measurement) is a fundamental type of measurement in quantum mechanics in which the state of a system is projected onto an eigenstate of an observable. Projective measurements represent the simplest and most idealized form of quantum measurement and form the basis for more general frameworks such as positive operator-valued measurements (POVMs) and quantum instruments. A projective measurement (also called a von Neumann measurement) is a fundamental type of measurement in quantum mechanics in which the state of a system is projected onto an eigenstate of an observable. Projective measurements represent the simplest and most idealized form of quantum measurement and form the basis for more general frameworks such as positive operator-valued measurements (POVMs) and quantum instruments.

	Projective measurements represent the simplest and most idealized form of quantum measurement and form the basis for more general frameworks such as [[positive operator-valued ~~measurement]]s~~ (POVMs) and quantum instruments.<ref name=Nielsen>{{cite book \|last1=Nielsen \|first1=Michael A. \|last2=Chuang \|first2=Isaac L. \|title=Quantum Computation and Quantum Information \|publisher=Cambridge University Press \|year=2010}}</ref>
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	== Physical interpretation ==		== Physical interpretation ==
	Projective measurements correspond to ideal measurements in which the system is sharply projected onto an eigenstate of the observable. They are often associated with textbook examples such as spin measurements using a [[Stern–Gerlach experiment]].<ref name=Nielsen/>		Projective measurements correspond to ideal measurements in which the system is sharply projected onto an eigenstate of the observable. They are often associated with textbook examples such as spin measurements using a Stern–Gerlach experiment.<ref name=Nielsen/>

	However, real physical measurements are often more general and cannot always be described by simple projection operators.		However, real physical measurements are often more general and cannot always be described by simple projection operators.

Harold: Arrange page top as TOC lead image columns

2026-05-17T14:01:05Z

Arrange page top as TOC lead image columns

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			{{Short description\|Quantum Collection topic on Quantum Projective measurement}}

	{{Quantum book backlink\|Measurement and information}}		{{Quantum book backlink\|Measurement and information}}

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			__TOC__
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	A '''projective measurement''' (also called a '''von Neumann measurement''') is a fundamental type of measurement in [[quantum mechanics]] in which the state of a system is projected onto an eigenstate of an observable.<ref name=Neumann>{{cite book \|last=von Neumann \|first=John \|title=Mathematical Foundations of Quantum Mechanics \|year=1932}}</ref>		A '''projective measurement''' (also called a '''von Neumann measurement''') is a fundamental type of measurement in [[quantum mechanics]] in which the state of a system is projected onto an eigenstate of an observable.<ref name=Neumann>{{cite book \|last=von Neumann \|first=John \|title=Mathematical Foundations of Quantum Mechanics \|year=1932}}</ref>

	Projective measurements represent the simplest and most idealized form of quantum measurement and form the basis for more general frameworks such as [[positive operator-valued measurement]]s (POVMs) and quantum instruments.<ref name=Nielsen>{{cite book \|last1=Nielsen \|first1=Michael A. \|last2=Chuang \|first2=Isaac L. \|title=Quantum Computation and Quantum Information \|publisher=Cambridge University Press \|year=2010}}</ref>		Projective measurements represent the simplest and most idealized form of quantum measurement and form the basis for more general frameworks such as [[positive operator-valued measurement]]s (POVMs) and quantum instruments.<ref name=Nielsen>{{cite book \|last1=Nielsen \|first1=Michael A. \|last2=Chuang \|first2=Isaac L. \|title=Quantum Computation and Quantum Information \|publisher=Cambridge University Press \|year=2010}}</ref>
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			<div style="width:300px;">
			[[File:Quantum_projective_measurement_collapse_yellow.jpg\|thumb\|280px\|Quantum Projective measurement.]]
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	[[File:Quantum_projective_measurement_collapse_yellow.jpg\|thumb\|400px\|Projective measurement: a quantum state collapses onto one of the orthogonal eigenstates of the observable, yielding a definite outcome.]]		</div>

	== Definition ==		== Definition ==

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	{{Quantum book backlink\|Measurement and information}}		{{Quantum book backlink\|Measurement and information}}
	{{Quantum article nav\|previous=Physics:Quantum Measurement operators\|previous label=Measurement operators\|next=Physics:Quantum POVM\|next label=POVM}}		{{Quantum article nav\|previous=Physics:Quantum Measurement operators\|previous label=Measurement operators\|next=Physics:Quantum POVM\|next label=POVM}}