Computability in basic quantum mechanics

Neumann, Eike, Pape, Martin and Streicher, Thomas (2018). Computability in basic quantum mechanics. Logical Methods in Computer Science, 14 (2),

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.

Publication DOI: https://doi.org/10.23638/LMCS-14(2:14)2018
Divisions: Engineering & Applied Sciences > Computer science
Additional Information: Creative Commons Attribution Non-Commercial License. © E. Neumann, M. Pape, and T. Streicher
Uncontrolled Keywords: Theoretical Computer Science,Computer Science(all)
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
https://lmcs.ep ... iences.org/4598 (Publisher URL)
Published Date: 2018-06-19
Authors: Neumann, Eike
Pape, Martin
Streicher, Thomas

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