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Consistency of the Shannon entropy in quantum experiments
KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
2004 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 69, no 6, 062108- p.Article in journal (Refereed) Published
Abstract [en]

The consistency of the Shannon entropy, when applied to outcomes of quantum experiments, is analyzed. It is shown that the Shannon entropy is fully consistent and its properties are never violated in quantum settings, but attention must be paid to logical and experimental contexts. This last remark is shown to apply regardless of the quantum or classical nature of the experiments.

Place, publisher, year, edition, pages
2004. Vol. 69, no 6, 062108- p.
Keyword [en]
Composition; Entropy; Experiments; Mathematical operators; Matrix algebra; Probability distributions; Statistical methods; Thermodynamics; Conditional entropy; Cummutative property; Density matrix; Shannon entropy; Quantum theory
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-7279DOI: 10.1103/PhysRevA.69.062108ISI: 000222471400015Scopus ID: 2-s2.0-4043141550OAI: oai:DiVA.org:kth-7279DiVA: diva2:12241
Note
QC 20100816Available from: 2007-06-04 Created: 2007-06-04 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Studies in plausibility theory, with applications to physics
Open this publication in new window or tab >>Studies in plausibility theory, with applications to physics
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

The discipline usually called `probability theory' can be seen as the theory which describes and sets standard norms to the way we reason about plausibility. From this point of view, this `plausibility theory' is a province of logic, and the following informal proportion subsists:

plausibility theory is to the common notion of `plausibility', as deductive logic is to the common notion of `truth'.

Some studies in plausibility theory are here offered. An alternative view and mathematical formalism for the problem of induction (the prediction of uncertain events from similar, certain ones) is presented. It is also shown how from plausibility theory one can derive a mathematical framework, based on convex geometry, for the description of the predictive properties of physical theories. Within this framework, problems like state assignment - for any physical theory - find simple and clear algorithms, numerical examples of which are given for three-level quantum systems. Plausibility theory also gives insights on various fashionable theorems, like Bell’s theorem, and various fashionable `paradoxes', like Gibbs' paradox.

Place, publisher, year, edition, pages
Stockholm: KTH, 2007. xv, 105 p.
Series
Trita-ICT/MAP, 2007:6
Keyword
Bayesian probability theory, quantum theory, state assignment, state estimation
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-4421 (URN)978-91-7178-688-3 (ISBN)
Public defence
2007-06-12, D, Forum, Isafjordsgatan 39, Kista, 10:00
Opponent
Supervisors
Note
QC 20100816Available from: 2007-06-04 Created: 2007-06-04 Last updated: 2010-08-16Bibliographically approved

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