Interactive Leakage Chain Rule for Quantum Min-entropy

Abstract: 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.