Computability in basic quantum mechanics

Eike Neumann, Martin Pape, Thomas Streicher

Research output: Contribution to journalArticle

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 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.

Original languageEnglish
Article number14
JournalLogical Methods in Computer Science
Volume14
Issue number2
DOIs
Publication statusPublished - 19 Jun 2018

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Computability
Quantum theory
Hilbert spaces
Quantum Mechanics
Data structures
Spectral Theorem
Valuation
Hilbert
Data Structures
Hilbert space
Subspace
Closed

Bibliographical note

Creative Commons Attribution Non-Commercial License.
© E. Neumann, M. Pape, and T. Streicher

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Neumann, E., Pape, M., & Streicher, T. (2018). Computability in basic quantum mechanics. Logical Methods in Computer Science, 14(2), [14]. https://doi.org/10.23638/LMCS-14(2:14)2018
Neumann, Eike ; Pape, Martin ; Streicher, Thomas. / Computability in basic quantum mechanics. In: Logical Methods in Computer Science. 2018 ; Vol. 14, No. 2.
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Neumann, E, Pape, M & Streicher, T 2018, 'Computability in basic quantum mechanics', Logical Methods in Computer Science, vol. 14, no. 2, 14. https://doi.org/10.23638/LMCS-14(2:14)2018

Computability in basic quantum mechanics. / Neumann, Eike; Pape, Martin; Streicher, Thomas.

In: Logical Methods in Computer Science, Vol. 14, No. 2, 14, 19.06.2018.

Research output: Contribution to journalArticle

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Neumann E, Pape M, Streicher T. Computability in basic quantum mechanics. Logical Methods in Computer Science. 2018 Jun 19;14(2). 14. https://doi.org/10.23638/LMCS-14(2:14)2018