Work

A Collection of Pinsker-type Inequalities for Quantum Divergences

Year: 2026

Type: conference-paper

Abstract: Pinsker's inequality sets a lower bound on the Umegaki divergence of two quantum states in terms of their trace distance. In this work, we formulate corresponding estimates for a variety of quantum and classical divergences including $f$-divergences like Hellinger and $χ^2$-divergences as well as Rényi divergences and special cases thereof like the Umegaki divergence, collision divergence, max divergence. We further provide a strategy on how to adapt these bounds to smoothed divergences.

Source: IEEE International Symposium on Information Theory (ISIT)

DOI: 10.1109/isit62367.2026.11653926

Authors: Kläre Wienecke, Gereon Koßmann, René Schwonnek

Institutions: Leibniz University Hannover, RWTH Aachen University

Language: English

Topic: Quantum Information and Cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Bundesministerium für Bildung und Forschung, H2020 European Research Council

Awards: Entropy for Quantum Information Science, G40493870, G4285572622, EXC 2123: QuantumFrontiers Licht und Materie an der Quantengrenze, G745383156