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

Understand

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.