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arXiv · 1701.03195

Moderate Deviation Analysis for Classical-Quantum Channels and Quantum Hypothesis Testing

Hao-Chung Cheng·Min-Hsiu Hsieh
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Abstract

In this work, we study the tradeoffs between the error probabilities of classical-quantum channels and the blocklength $n$ when the transmission rates approach the channel capacity at a rate slower than $1/\sqrt{n}$, a research topic known as moderate deviation analysis. We show that the optimal error probability vanishes under this rate convergence. Our main technical contributions are a tight quantum sphere-packing bound, obtained via Chaganty and Sethuraman's concentration inequality in strong large deviation theory, and asymptotic expansions of error-exponent functions. Moderate deviation analysis for quantum hypothesis testing is also established. The converse directly follows from our channel coding result, while the achievability relies on a martingale inequality.

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Hao-Chung Cheng, Min-Hsiu Hsieh. 2017-01-12. Moderate Deviation Analysis for Classical-Quantum Channels and Quantum Hypothesis Testing. https://arxiv.org/abs/1701.03195

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