(New) 2 December 2024, KdVI General Mathematics Colloquium, Matthias Christandl

Quantum entropy (aka von Neumann entropy) is the quantum generalization of Shannon entropy. Its utility in quantum information theory parallels that of Shannon entropy in traditional information theory, thereby being a foundational concept for the field. Of particular importance are the relations of the quantum entropies of a larger system and its individual parts. Finding all of them would be settling the 'laws of quantum information theory' (Pippenger). So how far have we come?

No prior knowledge in quantum information or even classical information theory is assumed. I will point out some relations to linear algebra, functional analysis, symplectic geometry and representation theory. The closure of the mentioned relations form a cone. The patient listener will be looking forward to a filled version of one