Classical and Quantum Information Measures Characterizing Convertibility: An Axiomatic Approach
Abstract
In this PhD thesis, we take an axiomatic approach to studying multivariate divergences, which are measures of the information content of a tuple of classical or quantum states. These divergences are studied in the context of large-sample and catalytic convertibility of tuples of states. This type of convertibility is characterized by the ordering of an axiomatically defined family of divergences. In this thesis, we identify this family of divergences explicitly for two scenarios, one classical and one quantum. In the classical setting, we show that the relevant divergences are certain generalizations of the bivariate Rényi divergences. Unlike previous studies, we do not require the distributions to have the same support, yielding interesting new divergences. In the quantum setting, we consider pairs of classical-quantum states with pure component states, and find that majorization is characterized by all α-z relative entropies for α<1. This demonstrates the first operational interpretation of these relative entropies.
Related
- Characterizing nonlinear information in the linear sampling method for inverse medium scattering
- Scattering Measures and Information Geometry
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- Quantum information processing under maximal distance measures
- infomeasure-rs: A High-Performance Rust Library for Information-Theoretic Measures and Estimators
BibTeX
@misc{verhagen2026classical,
title = {{Classical and Quantum Information Measures Characterizing Convertibility: An Axiomatic Approach}},
author = {Frits Verhagen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16267},
eprint = {2610.16267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16267},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classical and Quantum Information Measures Characterizing Convertibility: An Axiomatic Approach
AU - Frits Verhagen
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16267
UR - https://arxiv.org/abs/2610.16267
AB - In this PhD thesis, we take an axiomatic approach to studying multivariate divergences, which are measures of the information content of a tuple of classical or quantum states. These divergences are studied in the context of large-sample and catalytic convertibility of tuples of states. This type of convertibility is characterized by the ordering of an axiomatically defined family of divergences. In this thesis, we identify this family of divergences explicitly for two scenarios, one classical and one quantum. In the classical setting, we show that the relevant divergences are certain generalizations of the bivariate Rényi divergences. Unlike previous studies, we do not require the distributions to have the same support, yielding interesting new divergences. In the quantum setting, we consider pairs of classical-quantum states with pure component states, and find that majorization is characterized by all α-z relative entropies for α<1. This demonstrates the first operational interpretation of these relative entropies.
ER -