# Quantum Markov Semigroups with detailed balance as gradient flow for relative entropy and entropy production inequalities

Tuesday, October 24, 2017 -

4:30pm to 5:30pm

Semigroups of completely positive trace preserving maps satisfying a certain detailed balance condition are gradient flow driven by dissipation of the quantum relative entropy with respect to a non-commutative analog of the 2-Wasserstein metric on the space of probability densities on Euclidean space. As in the classical case, this way of viewing the evolution equations solved by these semigroups leads to sharp entropy production inequalities. This perspective has resolved some recent conjectures in quantum information theory. This is joint work with Jan Maas.

Speaker:

Eric Carlen

Rutgers University

Event Location:

Jadwin Hall 343