Document Type
Article
Publication Date
2-2013
Publication Source
Mathematical Structures in Computer Science
Abstract
In this paper we extend the spectral order of Coecke and Martin to infinite-dimensional quantum states. Many properties present in the finite-dimensional case are preserved, but some of the most important are lost. The order is constructed and its properties analysed. Most of the useful measurements of information content are lost. Shannon entropy is defined on only a part of the model, and that part is not a closed subset of the model. The finite parts of the lattices used by Birkhoff and von Neumann as models for classical and quantum logic appear as subsets of the models for infinite classical and quantum states.
Inclusive pages
95-130
ISBN/ISSN
0960-1295
Document Version
Postprint
Copyright
Copyright © 2012, Cambridge University Press.
Publisher
Cambridge University Press
Volume
23
Issue
1
Peer Reviewed
yes
eCommons Citation
Mashburn, Joe, "A Spectral Order for Infinite Dimensional Quantum Spaces" (2013). Mathematics Faculty Publications. 16.
https://ecommons.udayton.edu/mth_fac_pub/16
Comments
Article available for download is the author's accepted manuscript; some differences may exist between this version and the published version; as such, researchers wishing to quote directly from this source are advised to consult the version of record, available online.
Permission documentation is on file.