From Renyi Entropy Power to Information Scan of Quantum States

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

From Renyi Entropy Power to Information Scan of Quantum States

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

From Renyi Entropy Power to Information Scan of Quantum States

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA19-16066S" target="_blank" >GA19-16066S: Nelineární interakce a přenos informace v komplexních systémech s extrémními událostmi</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Entropy

ISSN

1099-4300

e-ISSN

1099-4300

Svazek periodika

23

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

24

Strana od-do

—

Kód UT WoS článku

000633577600001

EID výsledku v databázi Scopus

2-s2.0-85102940781