Computability in Basic Quantum Mechanics

Neumann, Eike; Pape, Martin; Streicher, Thomas

doi:10.23638/LMCS-14(2:14)2018

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Computability in Basic Quantum Mechanics

Eike Neumann, Martin Pape, Thomas Streicher

Logical Methods in Computer Science, Volume: 14, Issue: 2

Swansea University Author: Eike Neumann

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DOI (Published version): 10.23638/LMCS-14(2:14)2018

Abstract

The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space H. In terms of the Hilbert lattice L of closed linear subspaces of H the notions of state and observable can be formulated as kinds of measures as in [21]. The aim of this paper is to show...

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Published in:	Logical Methods in Computer Science
ISSN:	1860-5974
Published:	2018
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa60139
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first_indexed	2022-06-07T12:17:17Z
last_indexed	2023-01-11T14:41:54Z
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spelling	2022-07-07T11:20:57.1430098 v2 60139 2022-06-07 Computability in Basic Quantum Mechanics 1bf535eaa8d6fcdfbd464a511c1c0c78 Eike Neumann Eike Neumann true false 2022-06-07 SCS The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space H. In terms of the Hilbert lattice L of closed linear subspaces of H the notions of state and observable can be formulated as kinds of measures as in [21]. The aim of this paper is to show that there is a good notion of computability for these data structures in the sense of Weihrauch's Type Two Effectivity (TTE) [26]. Instead of explicitly exhibiting admissible representations for the data types under consideration we show that they do live within the category QCB0 which is equivalent to the category AdmRep of admissible representations and continuously realizable maps between them. For this purpose in case of observables we have to replace measures by valuations which allows us to prove an effective version of von Neumann's Spectral Theorem. Journal Article Logical Methods in Computer Science 14 2 1860-5974 19 6 2018 2018-06-19 10.23638/LMCS-14(2:14)2018 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2022-07-07T11:20:57.1430098 2022-06-07T13:13:15.4543042 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Eike Neumann 1 Martin Pape 2 Thomas Streicher 3 60139__24471__20f7c590481646e09513131ea191da9e.pdf 60139_VoR.pdf 2022-07-07T11:19:18.9733962 Output 444299 application/pdf Version of Record true Copyright: E. Neumann, M. Pape, and T. Streicher. This work is licensed under the Creative Commons Attribution License. To view a copy of this license true eng https://creativecommons.org/licenses/by/4.0/
title	Computability in Basic Quantum Mechanics
spellingShingle	Computability in Basic Quantum Mechanics Eike Neumann
title_short	Computability in Basic Quantum Mechanics
title_full	Computability in Basic Quantum Mechanics
title_fullStr	Computability in Basic Quantum Mechanics
title_full_unstemmed	Computability in Basic Quantum Mechanics
title_sort	Computability in Basic Quantum Mechanics
author_id_str_mv	1bf535eaa8d6fcdfbd464a511c1c0c78
author_id_fullname_str_mv	1bf535eaa8d6fcdfbd464a511c1c0c78_***_Eike Neumann
author	Eike Neumann
author2	Eike Neumann Martin Pape Thomas Streicher
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container_title	Logical Methods in Computer Science
container_volume	14
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publishDate	2018
institution	Swansea University
issn	1860-5974
doi_str_mv	10.23638/LMCS-14(2:14)2018
college_str	Faculty of Science and Engineering
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description	The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space H. In terms of the Hilbert lattice L of closed linear subspaces of H the notions of state and observable can be formulated as kinds of measures as in [21]. The aim of this paper is to show that there is a good notion of computability for these data structures in the sense of Weihrauch's Type Two Effectivity (TTE) [26]. Instead of explicitly exhibiting admissible representations for the data types under consideration we show that they do live within the category QCB0 which is equivalent to the category AdmRep of admissible representations and continuously realizable maps between them. For this purpose in case of observables we have to replace measures by valuations which allows us to prove an effective version of von Neumann's Spectral Theorem.
published_date	2018-06-19T04:18:00Z
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Computability in Basic Quantum Mechanics

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