|Strong Converse Bounds in Quantum Network Information Theory
|Hao-Chung Cheng, Nilanjana Datta, University of Cambridge, United Kingdom; Cambyse Rouzé, Technische Universität München, Germany
|Q.6: Quantum Networks
|Quantum Systems, Codes, and Information
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|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, and properties of the projectively measured R\'enyi 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.