Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

A family of generalized quantum entropies: definition and properties

Bosyk, Gustavo Martin, Steeve Zozor, Federico Holik, Portesi, Mariela Adelina, Lamberti, Pedro Walter

Published Aug 1, 2016• 33 citations
OpenAlex

Related papers

A family of generalized quantum entropies: definition and properties

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

arXiv:1506.02090•Quantum Information Processing•May 7, 2016•48 citations

On quantum Renyi entropies: a new definition and some properties.

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

•Jun 13, 2013•26 citations

Generalized quantum entropies: a definition and some properties

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

In this presentation, a family of quantum entropies inspired by the clasical (h,φ)- entropies proposed by Salicrú et al. (more precisely, inspired by the Csiszár’s divergen- cies) will be introduced. The proposed family includes several well-known entropies such that the von Neumann entropy or quantum versions of the Rényi’s and Havrda- Charvát-Daróczy-Tsallis’s entropies, among many others. The main properties of the proposed quantum (h, φ )-entropies lie on the the fundamental concept of majorization. The behavior of these entropies when a quantum state is subject to some quantum op- erations (unitary, measurement) will be characterized, and its behavior when dealing with composite systems as well. Some potential applications in detection of entan- glement will be exposed. Finally, we will present possible definitions of associate measures such that conditional generalized quantum entropies.

•Nov 3, 2016•0 citations

Generalized quantum entropies

Adriana Paula Batista dos Santos, R. Silva, J. S. Alcaniz +1 more

Physics Letters A•Jul 10, 2011•8 citations

Entropies of general quantum states

Naohumi Muraki, Masanori Ohya, Dėnes Petz

Open Systems & Information Dynamics•Apr 1, 1992•31 citations

On quantum R\'enyi entropies: a new definition, some properties and several conjectures

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

The R\'enyi 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 R\'enyi 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 R\'enyi entropies and the corresponding relative entropies that contains the min-entropy, collision entropy, von Neumann entropy as well as 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 and a limited duality relation. We conclude that the treatment of these entropies is technically challenging and requires sophisticated tools from linear algebra. We share several conjectured properties which we were unable to prove.

•Jun 13, 2013•7 citations
In this presentation, a family of quantum entropies inspired by the clasical (h,φ)- entropies proposed by Salicrú et al. (more precisely, inspired by the Csiszár’s divergen- cies) will be introduced. The proposed family includes several well-known entropies such that the von Neumann entropy or quantum versions of the Rényi’s and Havrda- Charvát-Daróczy-Tsallis’s entropies, among many others. The main properties of the proposed quantum (h, φ )-entropies lie on the the fundamental concept of majorization. The behavior of these entropies when a quantum state is subject to some quantum op- erations (unitary, measurement) will be characterized, and its behavior when dealing with composite systems as well. Some potential applications in detection of entan- glement will be exposed. Finally, we will present possible definitions of associate measures such that conditional generalized quantum entropies.
The R\'enyi 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 R\'enyi 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 R\'enyi entropies and the corresponding relative entropies that contains the min-entropy, collision entropy, von Neumann entropy as well as 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 and a limited duality relation. We conclude that the treatment of these entropies is technically challenging and requires sophisticated tools from linear algebra. We share several conjectured properties which we were unable to prove.