Moderate deviation analysis for classical-quantum channels and quantum hypothesis testing
Journal
IEEE Transactions on Information Theory
Journal Volume
64
Journal Issue
2
Pages
1385-1403
Date Issued
2018
Author(s)
Abstract
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 {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. ? 1963-2012 IEEE.
Subjects
Channel capacity; Channel coding; Dispersion (waves); Entropy; Errors; Probability; Quantum entanglement; Quantum theory; Reliability; Testing; Asymptotic expansion; Classical-quantum channels; Concentration inequality; Error probabilities; Large deviation theory; Martingale inequalities; Sphere packing bound; Technical contribution; Communication channels (information theory)
Type
journal article