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

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.

See also concurrent work (arXiv:1701.03114) by Christopher Chubb, Vincent Tan, and Marco Tomamichel. Typos are corrected in v2

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• On the strong converses for the quantum channel capacity theorems
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Cited by in corpus (4)

• Semidefinite programming strong converse bounds for classical capacity
• Beyond the thermodynamic limit: finite-size corrections to state interconversion rates
• Beating the Classical Limits of Information Transmission using a Quantum Decoder
• Finite blocklength and moderate deviation analysis of hypothesis testing of correlated quantum states and application to classical-quantum channels with memory