ResearchCryptography Information Theory Foundations
Quantum CryptographyQuantum communication offers significant advantages when it comes to achieving cryptographic security. The classical example is quantum key distribution which allows two distant parties to establish a secure key. However, quantum communication can also help us to solve many other cryptographic problems. One of the things that we are interested in is the question of what resources allow us to solve cryptographic tasks between two parties who do not trust each other such as bit commitment, oblivious transfer or secure identifcation. For example, we introduced and work on the so-called noisy-storage model. Recent work examines the power of relativity for cryptography. A question that we are particularly excited about right now is whether we can develop a very general resource theory for quantum cryptography which tells us what kind of output states can be obtained from particular input states in the presence of cheating parties.
Quantum Information TheoryQuantum information differs signficantly from classical information and the presence of entanglement has often thwarted our classical intuition. Our goal is to determine and understand the extend of this difference. On the one hand, we are interested in understanding communication aspects of quantum information, that is, quantum information theory. For example, we would like to understand limits to a quantum channels ability to transmit information, i.e., its capacity. To this end, we have tried to tackle the problem from the opposite end and derived several strong converses for channel coding which determine sharp limits on our ability to send any information.
On the other hand, we are interested in what our newfound knowledge of how information behaves in small systems can tell us about physics itself. One thing that we are presently quite excited about is to investigate what quantum information theory can tell us about the foundations of statistical mechanics.