Second order asymptotics of visible mixed quantum source coding via universal codes
Abstract
The simplest example of a quantum information source with memory is a mixed source which emits signals entirely from one of two memoryless quantum sources with given a priori probabilities. Considering a mixed source consisting of a general one-parameter family of memoryless sources, we derive the second order asymptotic rate for fixed-length visible source coding. Furthermore, we specialize our main result to a mixed source consisting of two memoryless sources. Our results provide the first example of second order asymptotics for a quantum information-processing task employing a resource with memory. For the case of a classical mixed source (using a finite alphabet), our results reduce to those obtained by Nomura and Han [IEEE Trans. on Inf. Th. 59.1 (2013), pp. 1-16]. To prove the achievability part of our main result, we introduce universal quantum source codes achieving second order asymptotic rates. These are obtained by an extension of Hayashi's construction [IEEE Trans. on Inf. Th. 54.10 (2008), pp. 4619-4637] of their classical counterparts.
Cite
@article{arxiv.1407.6616,
title = {Second order asymptotics of visible mixed quantum source coding via universal codes},
author = {Felix Leditzky and Nilanjana Datta},
journal= {arXiv preprint arXiv:1407.6616},
year = {2016}
}
Comments
18 pages, 1 figure; v2: slight changes in notation; v3: corrected an error in previous version; v4: new title, introduced universal codes achieving second order rate, paper greatly shortened and streamlined; v5: accepted for publication in IEEE Transactions on Information Theory, title slightly changed, main result is now for general one-parameter family of memoryless sources