Chain rules for quantum Rényi entropies

Journal Article · Sun Feb 15 00:00:00 EST 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4907981· OSTI ID:22403102

Dupuis, Frédéric ^[1]

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1. Faculty of Informatics, Masaryk University, Brno (Czech Republic)

We present chain rules for a new definition of the quantum Rényi conditional entropy sometimes called the “sandwiched” Rényi 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 Rényi entropy, this relation no longer holds as an equality but survives as an inequality of the form H{sub α}(AB|C) ⩾ H{sub β}(A|BC) + H{sub γ}(B|C), where the parameters α, β, γ obey the relation (α)/(α−1) =(β)/(β−1) +(γ)/(γ−1) and (α − 1)(β − 1)(γ − 1) > 1; if (α − 1)(β − 1)(γ − 1) < 1, the direction of the inequality is reversed.

• OSTI ID: 22403102
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ENTROPY
EQUATIONS
INFORMATION THEORY
QUANTUM MECHANICS