On quantum Rényi entropies: A new generalization and some properties
Abstract
The Renyi 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 Renyi entropies to the quantum setting have been proposed, most notably Petz's quasi-entropies and Renner's conditional min-, max- and collision entropy. Here, we argue that previous quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Renyi 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.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- December 2013
- DOI:
- 10.1063/1.4838856
- arXiv:
- arXiv:1306.3142
- Bibcode:
- 2013JMP....54l2203M
- Keywords:
-
- 05.70.Ce;
- 03.65.Ta;
- Thermodynamic functions and equations of state;
- Foundations of quantum mechanics;
- measurement theory;
- Quantum Physics;
- Computer Science - Information Theory;
- Mathematical Physics
- E-Print:
- v1: contains several conjectures