Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chapter 2 : Measurements (Axiom 1)

シロウ イシカワ, Shiro Ishikawa, 史郎 石川

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

2.1 Mathematical preparations 2.2 Observables 2.3 The meanings of observables and crisp observables 2.4 Measurement (Axiom 1) 2.5 Remarks 2.6 Examples 2.7 Operations of observables 2.8 Frequency probabilities 2.9 Appendix (Bell's thought experiment)

Related papers

Chapter 3 : The relation among systems (Axiom 2)

シロウ イシカワ, Shiro Ishikawa, 史郎 石川

3.1 Newton Equation and Schrödinger equation 3.2 The relation among systems (Definition) 3.3 Examples (Several tree structures) 3.4 The relation among systems (Axiom 2) 3.5 Heisenberg picture and Schrödinger picture 3.6 Measurability theorem 3.7 Appendix (Bell's inequality)

•Jan 1, 2006•0 citations

Mathematical Background

F. S. Levin

The quantities in physics that can be measured are conventionally denoted observables : entities that can be observed (directly or indirectly) and to which a value in appropriate units can be assigned. Examples include position, momentum, and energy. Unlike in classical physics, the concept of an observable in quantum theory possesses a significance beyond that of the measurable: to each observable there corresponds a unique operator in an abstract, linear vector space. These operators (and others) govern all aspects of quantum systems. Quantum operators act on abstract vectors in the linear space. Especially important are the eigenvectors and eigenvalues of these operators, in particular because some of the eigenvectors are the quantum states mentioned in the preceding chapters. Furthermore, for any operator that is the mathematical image of an observable, its eigenvalues constitute the entire set of values that measurement of the observable can yield . Finally, from the quantum states one can obtain the probabilities for the occurrence of events in the microscopic world, for example, the most likely value that measurement of an observable will yield. The concepts of operators and eigenvalue problems, as well as those of quantal probabilities, of Hermiticity, and of complete sets, were encountered and exemplified in the preceding chapter using the language of differential equations. While much of quantum mechanics could be presented in terms of this language alone, certain fundamental concepts (spin, for instance) cannot be, and it eventually becomes necessary to consider quantum mechanics as a theoretical framework embedded in that abstract linear vector space known as a Hilbert space.

Cambridge University Press eBooks•Dec 3, 2001•0 citations

Probability and measurement

Kenichi Konishi, Giampiero Paffuti

Abstract In this chapter we shall discuss these and related questions. We shall summarize what is well established and what has been clarified in the last several decades concerning these issues, trying to distinguish as clearly as possible different issues which are all called the “measurement problem”, and in each case, making an effort to clarify as sharply as possible the nature of the problem.

•Mar 5, 2009•0 citations

Making Mistakes Saves the Single World of the Extended Wigner’s Friend Experiment

Szymon Łukaszyk

Abstract The Extended Wigner’s Friend thought experiment comprising a quantum system containing an agent who draws conclusions, upon observing the outcome of a measurement of a qubit prepared in two non-orthogonal versions by another agent led its authors to conclude that quantum theory cannot consistently describe the use of itself. It has also been proposed that this thought experiment is equivalent to coherent entangled state (Bell type) experiments. It is argued in this paper that the assumption of the freedom of choice of the first Wigner’s friend invalidates such equivalency. It is also argued that the assumption of locality (physical space) introduces superfluous identity of indiscernibles metric axiom, which is invalid in quantum domain and generally disproven by the Ugly duckling mathematical theorem.

•Jan 27, 2021•1 citation

Chapter 6 : Fisher's statistics II (related to Axioms 1 and 2)

シロウ イシカワ, Shiro Ishikawa, 史郎 石川

6.1 Regression analysis I 6.2 Bayes operator, Schrödinger picture, and S-states 6.3 Regression analysis II in measurements 6.4 Conclusions

•Jan 1, 2006•0 citations

Chapter 12 : Heisenberg's uncertainty relation

シロウ イシカワ, Shiro Ishikawa, 史郎 石川

12.1 Introduction 12.2 Example due to Arthurs-Kelley 12.3 Approximate simultaneous measurement 12.4 Lemmas 12.5 Existence theorem 12.6 Uncertainty relations 12.7 EPR-experiment and Heisenberg's uncertainty relation

•Jan 1, 2006•0 citations
The quantities in physics that can be measured are conventionally denoted observables : entities that can be observed (directly or indirectly) and to which a value in appropriate units can be assigned. Examples include position, momentum, and energy. Unlike in classical physics, the concept of an observable in quantum theory possesses a significance beyond that of the measurable: to each observable there corresponds a unique operator in an abstract, linear vector space. These operators (and others) govern all aspects of quantum systems. Quantum operators act on abstract vectors in the linear space. Especially important are the eigenvectors and eigenvalues of these operators, in particular because some of the eigenvectors are the quantum states mentioned in the preceding chapters. Furthermore, for any operator that is the mathematical image of an observable, its eigenvalues constitute the entire set of values that measurement of the observable can yield . Finally, from the quantum states one can obtain the probabilities for the occurrence of events in the microscopic world, for example, the most likely value that measurement of an observable will yield. The concepts of operators and eigenvalue problems, as well as those of quantal probabilities, of Hermiticity, and of complete sets, were encountered and exemplified in the preceding chapter using the language of differential equations. While much of quantum mechanics could be presented in terms of this language alone, certain fundamental concepts (spin, for instance) cannot be, and it eventually becomes necessary to consider quantum mechanics as a theoretical framework embedded in that abstract linear vector space known as a Hilbert space.
Abstract The Extended Wigner’s Friend thought experiment comprising a quantum system containing an agent who draws conclusions, upon observing the outcome of a measurement of a qubit prepared in two non-orthogonal versions by another agent led its authors to conclude that quantum theory cannot consistently describe the use of itself. It has also been proposed that this thought experiment is equivalent to coherent entangled state (Bell type) experiments. It is argued in this paper that the assumption of the freedom of choice of the first Wigner’s friend invalidates such equivalency. It is also argued that the assumption of locality (physical space) introduces superfluous identity of indiscernibles metric axiom, which is invalid in quantum domain and generally disproven by the Ugly duckling mathematical theorem.