  The leakage chain rule for quantum min-entropy quantifies the change of
min-entropy when one party gets additional leakage about the information
source. Herein we provide an interactive version that quantifies the change of
min-entropy between two parties, who share an initial classical-quantum state
and are allowed to run a two-party protocol. As an application, we prove new
versions of lower bounds on the complexity of quantum communication of
classical information.
