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

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.

Publisher

Cambridge University Press

Volume

23

Issue

1

Volume

23

Issue

1

Peer Reviewed

yes

Link to published version

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