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 oneparameter family of memoryless sources, we derive the second order asymptotic rate for fixedlength 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 informationprocessing 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. 116]. 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. 46194637] of their classical counterparts.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 DOI:
 10.48550/arXiv.1407.6616
 arXiv:
 arXiv:1407.6616
 Bibcode:
 2014arXiv1407.6616L
 Keywords:

 Quantum Physics
 EPrint:
 18 pages, 1 figure