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A spectral order for infinite-dimensional quantum spaces

Published online by Cambridge University Press:  10 July 2012

JOE MASHBURN
JOE MASHBURN*
Affiliation:
Department of Mathematics, University of Dayton, Dayton OH 45469-2316, U.S.A. Email: joe.mashburn@udayton.edu
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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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 23 , Issue 1 , February 2013 , pp. 95 - 130
Copyright
Copyright © Cambridge University Press 2012

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