Strong Converse Bounds in Quantum Network Information Theory

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, and properties of the projectively measured R?nyi relative entropies. We develop a novel technique to employ this result to find both finite blocklength and exponential strong converse bounds for the tasks of distributed quantum hypothesis testing with communication constraints for a classical-quantum state, quantum source coding with compressed classical side information, and classical-quantum degraded broadcast channel coding. A full version of this paper is accessible at: arXiv:1905.00873 and arXiv:1905.00874. ? 2020 IEEE.