From Renyi Entropy Power to Information Scan of Quantum States
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00352347" target="_blank" >RIV/68407700:21340/21:00352347 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.3390/e23030334" target="_blank" >https://doi.org/10.3390/e23030334</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/e23030334" target="_blank" >10.3390/e23030334</a>
Alternative languages
Result language
angličtina
Original language name
From Renyi Entropy Power to Information Scan of Quantum States
Original language description
In this paper, we generalize the notion of Shannon's entropy power to the Renyi-entropy setting. With this, we propose generalizations of the de Bruijn identity, isoperimetric inequality, or Stam inequality. This framework not only allows for finding new estimation inequalities, but it also provides a convenient technical framework for the derivation of a one-parameter family of Renyi-entropy-power-based quantum-mechanical uncertainty relations. To illustrate the usefulness of the Renyi entropy power obtained, we show how the information probability distribution associated with a quantum state can be reconstructed in a process that is akin to quantum-state tomography. We illustrate the inner workings of this with the so-called "cat states", which are of fundamental interest and practical use in schemes such as quantum metrology. Salient issues, including the extension of the notion of entropy power to Tsallis entropy and ensuing implications in estimation theory, are also briefly discussed.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
<a href="/en/project/GA19-16066S" target="_blank" >GA19-16066S: Nonlinear interactions and information transfer in complex systems with extreme events</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Entropy
ISSN
1099-4300
e-ISSN
1099-4300
Volume of the periodical
23
Issue of the periodical within the volume
3
Country of publishing house
CH - SWITZERLAND
Number of pages
24
Pages from-to
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UT code for WoS article
000633577600001
EID of the result in the Scopus database
2-s2.0-85102940781