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Extensions and restrictions of gener...

Steinberg, Jonathan.

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Extensions and restrictions of generalized probabilistic theories

Record Type:	Electronic resources : Monograph/item
Title/Author:	Extensions and restrictions of generalized probabilistic theories/ by Jonathan Steinberg.
Author:	Steinberg, Jonathan.
Published:	Wiesbaden :Springer Fachmedien Wiesbaden : : 2022.,
Description:	viii, 79 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Mathematical preliminaries -- Generalized probabilistic theories -- Sections and Subsystems -- Two-sections of Quantum mechanics -- Conclusion.
Contained By:	Springer Nature eBook
Subject:	Quantum theory - Mathematics. -
Online resource:	https://doi.org/10.1007/978-3-658-37581-2
ISBN:	9783658375812

Extensions and restrictions of generalized probabilistic theories
Steinberg, Jonathan.

Extensions and restrictions of generalized probabilistic theories[electronic resource] /by Jonathan Steinberg. - Wiesbaden :Springer Fachmedien Wiesbaden :2022. - viii, 79 p. :ill., digital ;24 cm. - BestMasters,2625-3615. - BestMasters..

Introduction -- Mathematical preliminaries -- Generalized probabilistic theories -- Sections and Subsystems -- Two-sections of Quantum mechanics -- Conclusion.

Generalized probabilistic theories (GPTs) allow us to write quantum theory in a purely operational language and enable us to formulate other, vastly different theories. As it turns out, there is no canonical way to integrate the notion of subsystems within the framework of convex operational theories. Sections can be seen as generalization of subsystems and describe situations where not all possible observables can be implemented. Jonathan Steinberg discusses the mathematical foundations of GPTs using the language of Archimedean order unit spaces and investigates the algebraic nature of sections. This includes an analysis of the category theoretic structure and the transformation properties of the state space. Since the Hilbert space formulation of quantum mechanics uses tensor products to describe subsystems, he shows how one can interpret the tensor product as a special type of a section. In addition he applies this concept to quantum theory and compares it with the formulation in the algebraic approach. Afterwards he gives a complete characterization of low dimensional sections of arbitrary quantum systems using the theory of matrix pencils. About the author Jonathan Steinberg studied physics and mathematics at the university of Siegen and obtained his M. Sc. in the field of quantum foundations. Currently he investigates the relation between tensor eigenvalues and the quantification of multipartite entanglement under the tutelage of Prof. Otfried Guhne.

ISBN: 9783658375812

Standard No.: 10.1007/978-3-658-37581-2doiSubjects--Topical Terms:

705044
Quantum theory
--Mathematics.

LC Class. No.: QC174.17.M35 / S74 2022

Dewey Class. No.: 530.12

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505 0 $a Introduction -- Mathematical preliminaries -- Generalized probabilistic theories -- Sections and Subsystems -- Two-sections of Quantum mechanics -- Conclusion.
520 $a Generalized probabilistic theories (GPTs) allow us to write quantum theory in a purely operational language and enable us to formulate other, vastly different theories. As it turns out, there is no canonical way to integrate the notion of subsystems within the framework of convex operational theories. Sections can be seen as generalization of subsystems and describe situations where not all possible observables can be implemented. Jonathan Steinberg discusses the mathematical foundations of GPTs using the language of Archimedean order unit spaces and investigates the algebraic nature of sections. This includes an analysis of the category theoretic structure and the transformation properties of the state space. Since the Hilbert space formulation of quantum mechanics uses tensor products to describe subsystems, he shows how one can interpret the tensor product as a special type of a section. In addition he applies this concept to quantum theory and compares it with the formulation in the algebraic approach. Afterwards he gives a complete characterization of low dimensional sections of arbitrary quantum systems using the theory of matrix pencils. About the author Jonathan Steinberg studied physics and mathematics at the university of Siegen and obtained his M. Sc. in the field of quantum foundations. Currently he investigates the relation between tensor eigenvalues and the quantification of multipartite entanglement under the tutelage of Prof. Otfried Guhne.
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