Relating different quantum generalizations of the conditional Rényi entropy

Journal Article · Fri Aug 15 04:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4892761· OSTI ID:22306091

Tomamichel, Marco ^[1]; Berta, Mario ^[2]; Hayashi, Masahito ^[1]

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1. Centre for Quantum Technologies, National University of Singapore, Singapore 117543 (Singapore)
2. Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125 (United States)

Recently a new quantum generalization of the Rényi divergence and the corresponding conditional Rényi entropies was proposed. Here, we report on a surprising relation between conditional Rényi entropies based on this new generalization and conditional Rényi entropies based on the quantum relative Rényi entropy that was used in previous literature. Our result generalizes the well-known duality relation H(A|B) + H(A|C) = 0 of the conditional von Neumann entropy for tripartite pure states to Rényi entropies of two different kinds. As a direct application, we prove a collection of inequalities that relate different conditional Rényi entropies and derive a new entropic uncertainty relation.

• OSTI ID: 22306091
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 55; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ENTROPY
PROBABILITY
PURE STATES
QUANTUM MECHANICS
UNCERTAINTY PRINCIPLE