Algebras of measurements: The logical structure of quantum mechanics

Daniel Lehmann; Kurt Engesser; Dov M. Gabbay

doi:10.1007/s10773-006-9062-y

Algebras of measurements: The logical structure of quantum mechanics

Daniel Lehmann^*
, Kurt Engesser
, Dov M. Gabbay

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In quantum physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute.

Original language	English
Pages (from-to)	715-741
Number of pages	27
Journal	International Journal of Theoretical Physics
Volume	45
Issue number	4
DOIs	https://doi.org/10.1007/s10773-006-9062-y
State	Published - Apr 2006

Keywords

Measurement algebras
Quantum logic
Quantum measurements

Access to Document

10.1007/s10773-006-9062-y

Cite this

@article{fbef676fb7c043a9ba79e05555a0eaf9,

title = "Algebras of measurements: The logical structure of quantum mechanics",

abstract = "In quantum physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute.",

keywords = "Measurement algebras, Quantum logic, Quantum measurements",

author = "Daniel Lehmann and Kurt Engesser and Gabbay, \{Dov M.\}",

year = "2006",

month = apr,

doi = "10.1007/s10773-006-9062-y",

language = "אנגלית",

volume = "45",

pages = "715--741",

journal = "International Journal of Theoretical Physics",

issn = "0020-7748",

publisher = "Springer New York",

number = "4",

}

TY - JOUR

T1 - Algebras of measurements

T2 - The logical structure of quantum mechanics

AU - Lehmann, Daniel

AU - Engesser, Kurt

AU - Gabbay, Dov M.

PY - 2006/4

Y1 - 2006/4

N2 - In quantum physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute.

AB - In quantum physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute.

KW - Measurement algebras

KW - Quantum logic

KW - Quantum measurements

UR - https://www.scopus.com/pages/publications/33745805393

U2 - 10.1007/s10773-006-9062-y

DO - 10.1007/s10773-006-9062-y

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:33745805393

SN - 0020-7748

VL - 45

SP - 715

EP - 741

JO - International Journal of Theoretical Physics

JF - International Journal of Theoretical Physics

IS - 4

ER -

Algebras of measurements: The logical structure of quantum mechanics

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this