The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data-processing inequalities, a duality relation, and an entropic uncertainty relation.
Additional Metadata
MSC Information theory, general (msc 94A15), General mathematical topics and methods in quantum theory (msc 81Qxx)
THEME Other (theme 6)
Publisher American Institute of Physics
Persistent URL
Journal Journal of Mathematical Physics
Project Quantum Cryptography
Mueller-Lennert, M, Dupuis, F, Szehr, O, Fehr, S, & Tomamichel, M. (2013). On quantum Rényi Entropies: A New Generalization and some Properties. Journal of Mathematical Physics, 54. doi:10.1063/1.4838856