Information entropy and the space of decoherence functions in generalized quantum theory

CJ Isham*, N Linden

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)

Abstract

In standard quantum theory, the ideas of information entropy and of pure states are closely linked. States are represented by density matrices rho on a Hilbert space and the information entropy - tr(rho In rho) is minimized on pure states (pure states are the vertices of the boundary of the convex set of states). The space of decoherence functions in the consistent histories approach to generalized quantum theory is also a convex set. However, by showing that every decoherence function can be written as a convex combination of two other decoherence functions; we demonstrate that there are no ''pure'' decoherence functions. The main content of the paper is a notion of information entropy in generalized quantum mechanics which is applicable in contexts in which there is no a priori notion of time. Information entropy is defined first on consistent sets and then we show that it decreases upon refinement of the consistent set. This information entropy suggests an intrinsic way of giving a consistent set selection criterion.

Original languageEnglish
Pages (from-to)4030-4040
Number of pages11
JournalPhysical Review A: Atomic, Molecular and Optical Physics
Volume55
Issue number6
Publication statusPublished - Jun 1997

Keywords

  • LOGICAL REFORMULATION
  • MECHANICS
  • HISTORIES

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