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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2014
- DOI:
- 10.48550/arXiv.1407.6616
- arXiv:
- arXiv:1407.6616
- Bibcode:
- 2014arXiv1407.6616L
- Keywords:
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- Quantum Physics
- E-Print:
- 18 pages, 1 figure