Quantum conditional entropies from convex trace functionals
Quantum Physics
2026-03-17 v3
Abstract
We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity results for these functionals, we establish data-processing inequalities and additivity properties for our entropies, demonstrating their operational significance. We further prove completeness under duality, chain rules, and various monotonicity properties for this family. Our proofs draw on tools from complex interpolation theory, multivariate Araki--Lieb and Lieb--Thirring inequalities, variational characterizations of trace functionals, and spectral pinching techniques.
Cite
@article{arxiv.2410.21976,
title = {Quantum conditional entropies from convex trace functionals},
author = {Roberto Rubboli and Milad M. Goodarzi and Marco Tomamichel},
journal= {arXiv preprint arXiv:2410.21976},
year = {2026}
}