Generalized quantum entropies

Fabio Benatti

Xinhua Hu, Zhongxing Ye

The generalized quantum entropies are introduced in this paper. Some important properties such as nonnegativity, continuity, and concavity are proved. But different from the Von Neumann entropy, the subadditivity and additivity fail for the quantum unified (r,s)-entropy in general.

Sarah Chehade, Anna Vershynina

Gen Kimura, Junji Ishiguro, Makoto Fukui

General probabilistic theories are designed to provide operationally the most general probabilistic models including both classical and quantum theories. In this paper, we introduce a systematic method to construct a series of entropies, all of which generalize Shannon entropy in classical systems and von Neumann entropy in quantum systems. Using these entropies, the Holevo bound, an upper bound of the accessible information from a quantum system, is generalized to hold in any general probabilistic theory.

Martin Müller-Lennert, Frédéric Dupuis, Oleg Szehr +2 more

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.

G. M. Bosyk, Steeve Zozor, F. Holik +2 more