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Abstract

In this talk, I will first give a brief introduction of the information spectrum method, which was developed by Han-Verdu in the classical case and by Nagaoka-Hayashi in the quantum case, as a general approach in information theory. After the introduction, an information spectrum approach to classical-quantum channel resolvability is shown. Channel resolvability coding was proposed by Han-Verdu in the classical case, as a method to approximate or control output statistics of a given channel by choosing an appropriate ensemble of the channel input. Later Devetak applied channel resolvability implicitly to the study of the private capacity for c-q channels and developed the argument to relate the private capacity to the quantum capacity. Hayashi studied the theory of channel resolvability explicitly further both in the classical case and the quantum case. In this study, an improved non-asymptotic inequality for c-q channel resolvability is given. As a result, general formulas for c-q channel resolvability, the private capacity, and the quantum capacity are shown.