A smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels

Nilanjana Datta, Milan Mosonyi, Min Hsiu Hsieh, Fernando G.S.L. Brandao

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We use the smooth entropy approach to treat the problems of binary quantum hypothesis testing and the transmission of classical information through a quantum channel. We provide lower and upper bounds on the optimal type II error of quantum hypothesis testing in terms of the smooth max-relative entropy of the two states representing the two hypotheses. Then using a relative entropy version of the quantum asymptotic equipartition property (QAEP), we can recover the strong converse rate of the i.i.d. hypothesis testing problem in the asymptotics. On the other hand, combining Stein's lemma with our bounds, we obtain a stronger (ε-independent) version of the relative entropy-QAEP. Similarly, we provide bounds on the one-shot ε-error classical capacity of a quantum channel in terms of a smooth max-relative entropy variant of its Holevo capacity. Using these bounds and the ε-independent version of the relative entropy-QAEP, we can recover both the Holevo- Schumacher- Westmoreland theorem about the optimal direct rate of a memoryless quantum channel with product state encoding, as well as its strong converse counterpart.

Original languageEnglish
Article number6670246
Pages (from-to)8014-8026
Number of pages13
JournalIEEE Transactions on Information Theory
Volume59
Issue number12
DOIs
Publication statusPublished - Dec 1 2013

Keywords

  • Capacity
  • hypothesis testing
  • quantum channels
  • smooth max-relative entropy
  • strong converse

ASJC Scopus subject areas

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

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