Sharp and unsharp quantum effects
type: Item
instance of: scholarly article
title: Sharp and unsharp quantum effects
zbMATH Open document ID: 0913.46062
published in: Advances in Applied Mathematics
publication date: 1999-06-07T00:00:00Z
review text: This paper presents a survey of the work done on classical and quantum measurement theory over the past thirty years, distinguishing between the so-called ``sharp'' theory based upon repeatable operations and the so-called ``fuzzy'' theory based upon non-repeatable operations. Elementary operations on a physical system can be modelled by contractive positive linear operators \(T\) on a GL-space \(V\) [cf. \textit{E. B. Davies} and \textit{J. T. Lewis}, Commun. Math. Phys. 17, 239-260 (1970; Zbl 0194.58304)]. When the adjoint \(T^*\) of \(T\) is applied to the order unit \(e\) in the dual unital GM-space \(V^*\), an element \(T^*e\) is created. Such an element is said to be an effect (of the operation \(T\)) and the set \(E\) of all such effects forms a subset of the order unit interval \([0,e]\) in \(V^*\). Such an object \(E\) has been algebraically axiomatized, and is known as an effect algebra. In this paper, the author remarks that the various measurement theories provide examples of effect algebras, and goes on to consider when tensor products of effect algebras may be formed, thereby relating his work to that of \textit{D. J. Foulis} and \textit{C. H. Randall} [`Interpretations and foundations of quantum theory', Proc. Conf., Marburg 1979, 9-20 (1981; Zbl 0495.03041)].
Mathematics Subject Classification ID: 46N50
Mathematics Subject Classification ID: 81P15
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 1221619
zbMATH Keywords: sharp theory based upon repeatable operations
zbMATH Keywords: fuzzy theory based upon non-repeatable operations
zbMATH Keywords: classical and quantum measurement theory
zbMATH Keywords: contractive positive linear operators
zbMATH Keywords: GL-space
zbMATH Keywords: tensor products of effect algebras
author: Stan Gudder
reviewed by: C. M. Edwards
MaRDI profile type: Publication
full work available at URL: aama.1997.0575
OpenAlex ID: W2016299318
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DOI: 10.1006/AAMA.1997.0575
description: scientific article; zbMATH DE number 1221619