IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
5 years ago

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

Min-Hsiu Hsieh, Hao-Chung Cheng,
In this paper, 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 lower 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.

Publisher URL: http://ieeexplore.ieee.org/document/8170230

DOI: 8170230

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