Strong converse bounds in quantum network information theory

In this paper, we develop the first method for finding strong converse bounds in quantum network information theory. The general scheme relies on a recently obtained result in the field of non-commutative functional inequalities, namely the tensorization property of quantum reverse hypercontractivity for the quantum depolarizing semigroup. We develop a novel technique to employ this result to find both finite blocklength and exponential strong converse bounds for the tasks of quantum source coding with compressed classical side information, and distributed quantum hypothesis testing with communication constraints for a classical-quantum state. In the classical setting, these two problems can be reformulated in a unified framework in terms of the so-called image-size characterization problem, which we extend to the classical-quantum setting. We also use this technique to establish analogous strong converse bounds in broadcast communication scenarios. In particular, we consider the transmission of classical information through a degraded broadcast channel, whose outputs are two quantum systems, with the state of one being a degraded version of the other. In establishing this last result, we prove a second-order Fano-type inequality, which is of independent interest. Our method to study strong converses has potential applications in other important tasks of quantum network information theory.