Abstract

Fully quantum conditional entropies play a central role in quantum information theory and cryptography, where they measure the uncertainty about a quantum system from the perspective of an observer with access to a potentially correlated system. Through a novel construction, we introduce a comprehensive family of conditional entropies that reveals a unified structure underlying all previously studied forms of quantum conditional Rényi entropies, organizing them within a cohesive mathematical framework. This new family satisfies a range of desiderata, including data processing inequalities, additivity under tensor products, duality relations, chain rules, concavity or convexity, and various parameter monotonicity relations. Our approach provides unified proofs that streamline and generalize prior, more specialized arguments. We also derive new insights into well-known quantities, such as Petz conditional entropies, particularly in the context of chain rules. We expect this family of entropies, along with our generalized chain rules, to find applications in quantum cryptography and information theory.

Personal information

Roberto Rubboli is a Ph.D. student at the Centre for Quantum Technologies (National University of Singapore) under the supervision of Prof. Marco Tomamichel. Previously, he completed a master’s in theoretical physics at the University of Bologna, Italy. His main focus is on the mathematical foundations of quantum information theory and its implications for quantum resource theories. Additionally, he also explores optimization methods for quantum information.