Chain rules for quantum Renyi entropies

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F15%3A00087732" target="_blank" >RIV/00216224:14330/15:00087732 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1063/1.4907981" target="_blank" >http://dx.doi.org/10.1063/1.4907981</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.4907981" target="_blank" >10.1063/1.4907981</a>

Result language
angličtina
Original language name
Chain rules for quantum Renyi entropies
Original language description
We present chain rules for a new definition of the quantum Renyi conditional entropy sometimes called the "sandwiched" Renyi conditional entropy. More precisely, we prove analogues of the equation H(AB|C) = H(A|BC) + H(B|C), which holds as an identity for the von Neumann conditional entropy. In the case of the Rnyi entropy, this relation no longer holds as an equality but survives as an inequality of the form H-alpha(AB|C) > H-beta(A|BC) + H-gamma(B|C), where the parameters alpha, beta, gamma obey the relation alpha/alpha-1 = beta/beta-1 + gamma/gamma-1 and (alpha - 1)(beta - 1)(gamma - 1) > 1; if (alpha - 1)(beta - 1)(gamma - 1) < 1, the direction of the inequality is reversed.
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/GAP202%2F12%2F1142" target="_blank" >GAP202/12/1142: Weak Sources of Entanglement and Randomness</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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