Classical channel coding benefited from a remarkably clear target: Shannon’s capacity formula. Quantum channel coding is less settled. Even for memoryless Pauli channels, the quantum capacity is not known in general, and the hashing bound can be far below the best known upper bounds.
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In this talk I will discuss how one principled method of how one can obtain achievable rates beyond the hashing bound. I will start from the basic Gottesman standard form for stabilizer codes and use it to give a coding-theoretic view of the obstruction. The main idea is to exploit degeneracy and channel transforms so that the effective uncertainty seen by the decoder is reduced. This leads naturally to constructions involving familiar objects from classical coding theory, including binary symmetric channels and LDGM-type matrices.
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The goal is not only to improve numerical lower bounds, but also to better understand what capacity-achieving constructions for quantum channels might have to look like. No prior background in quantum information will be assumed.
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Bio:Â Ruediger L. Urbanke is a professor in the School of Computer and Communication Sciences at EPFL, where he is a member of the Information Processing Group. He received the Dipl.-Ing. degree from the Vienna University of Technology in 1990, and the M.Sc. and Ph.D. degrees in Electrical Engineering from Washington University in St. Louis in 1992 and 1995, respectively. From 1995 to 1999 he was a member of the Mathematics of Communications Department at Bell Labs, before joining EPFL. He served as Dean of the School of Computer and Communication Sciences from 2021 to 2025 and was President of the IEEE Information Theory Society in 2017. He is co-author, with Tom Richardson, of Modern Coding Theory published by Cambridge University Press. His research interests include coding and information theory, error-correcting codes for classical and quantum communication, and the theoretical foundations of modern machine learning.