|Additivity in Classical-Quantum Wiretap Channels
|Arkin Tikku, School of Physics, University of Sydney, Australia; Joseph M. Renes, ETH Zürich, Switzerland; Mario Berta, Imperial College London, United Kingdom
|Q.7: Quantum Security
|Quantum Systems, Codes, and Information
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|Due to Csiszár and Körner, the capacity of classical wiretap channels has a single-letter characterisation in terms of the private information. For quantum wiretap channels, however, it is known that regularisation of the private information is necessary to reach the capacity. Here we study hybrid classical-quantum wiretap channels in order to resolve how much quantumness is needed to witness non-additivity phenomena in Shannon information theory. For wiretap channels with quantum inputs but classical outputs, we prove that the characterisation of the capacity in terms of the private information stays single-letter. Hence, entangled input states are of no asymptotic advantage in this setting. For wiretap channels with classical inputs, we show by means of explicit examples that the private information already becomes non-additive when either one of the two receivers becomes quantum (with the other receiver staying classical). This gives non-additivity examples that are not caused by entanglement and illustrates that in the wiretap model quantum adversaries are strictly different from classical adversaries.