Determination of bounds of the $beta$-entropic sum of two noncommuting variables.

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F01%3A00001226" target="_blank" >RIV/61989592:15310/01:00001226 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Determination of bounds of the $beta$-entropic sum of two noncommuting variables.
Original language description
This article deals with the Havrda-Charvat beta -entropy as a dispersion measure for the quantum observables. This entropy depends on a parameter beta and thus represents a set of uncertainty measures which includes the Shannon entropy as a special case.However, for certain values of beta, it is considerably simpler to handle mathematically than the Shannon entropy. It is possible, e.g. to find easier the bounds of the sum of beta -entropies for two noncommuting observables than the bounds of the sum of their Shannon entropies. By means of the variational method we determine such a probability distribution of noncommuting observables which minimizes or maximizes their beta -entropic sum. As an example, we compute the bounds of beta -entropic sum of the spin components of a spin-1/2 particle for the arbitrary beta, and two selected values of beta. Putting beta --> 1 in the beta -entropic sum we get the upper and lower bounds of their Shannon entropy sum.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Project
<a href="/en/project/GA202%2F01%2F1450" target="_blank" >GA202/01/1450: Quantum fluctuations in nonlinear lattice electron-phonon models in one dimension</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2001
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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