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arXiv · 1602.03297

On the Concavity of Auxiliary Function in Classical-Quantum Channels

Hao-Chung Cheng·Min-Hsiu Hsieh
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Abstract

The auxiliary function of a classical channel appears in two fundamental quantities that upper and lower bound the error probability, respectively. A crucial property of the auxiliary function is its concavity, which leads to several important results in finite block length analysis. In this paper, we prove that the auxiliary function of a classical-quantum channel also enjoys the same concave property, extending an earlier partial result to its full generality. The key component in our proof is a beautiful result of geometric means of operators.

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Hao-Chung Cheng, Min-Hsiu Hsieh. 2016-02-10. On the Concavity of Auxiliary Function in Classical-Quantum Channels. https://doi.org/10.1109/tit.2016.2598835

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