Second-Order Asymptotics of Visible Mixed Quantum Source Coding via Universal Codes

Felix Leditzky, Nilanjana Datta

Research output: Contribution to journalArticlepeer-review


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 the 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. To prove the achievability part of our main result, we introduce universal quantum source codes achieving the second-order asymptotic rates. These are obtained by an extension of Hayashi's construction of their classical counterparts.

Original languageEnglish (US)
Article number7476883
Pages (from-to)4347-4355
Number of pages9
JournalIEEE Transactions on Information Theory
Issue number7
StatePublished - Jul 2016
Externally publishedYes


  • Quantum information
  • information spectrum
  • mixed source
  • second order asymptotics
  • source coding

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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