Chain rules for quantum Renyi entropies

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Authors

DUPONT DUPUIS Frédéric

Year of publication 2015
Type Article in Periodical
Magazine / Source Journal of Mathematical Physics
MU Faculty or unit

Faculty of Informatics

Citation
Doi http://dx.doi.org/10.1063/1.4907981
Field Theoretical physics
Keywords quantum information; renyi entropy
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.
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