Quantum Information Theory

The Focus Group on Quantum Information Theory involves Hans Fischer Senior Fellow Prof. Andreas Winter (Universitat Autonoma de Barcelona) and his hosts Prof. Holger Boche (TUM School of Computation, Information and Technology) and Prof. Gerhard Kramer (Department of Electrical and Computer Engineering).

Secure data transfer today is largely based on complexity assumptions that might be rendered unreasonable by future quantum computers. Quantum communication opens up the possibility of physically verifiable privacy. But it offers many other potential applications and challenging theoretical problems. The standard approach to communication focuses on the transmission of messages, and in particular the notion of privacy is very much settled on a composable definition of statistical quality of secret keys. At the same time, few-user settings, such as Wyner’s wiretap channel, can be analysed using only the classic inequalities of the Shannon and von Neumann entropy in correlated systems. 

We are planning to branch out beyond the standard assumptions by considering security criteria in wiretap channels that are both weaker and more realistic than the standard setting. Likewise, we will develop a focus on identification via quantum channels, going beyond the Shannon paradigm, which offers many exciting open questions to work on. Finally, we will further quantum entropy inequalities beyond strong subadditivity; indeed, it is known since the 1990s that there are non-Shannon-type inequalities which govern classical network communication problems and multi-user secret sharing, but no such inequality has yet been proven for the von Neumann entropy, even though these classical inequalities have been conjectured to hold more generally fort he von Neumann entropy.

We hope that this research at the cutting edge of quantum information theory can feed into the existing important activities on 6G and molecular communication at the School of Computation, Information and Technology.

TUM-IAS funded doctoral candidate:

Pau Colomer, Chair of Theoretical Information Technology