On Composite Quantum Hypothesis Testing

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Mario Berta
  • Fernando G.S.L. Brandão
  • Christoph Hirche

External Research Organisations

  • Imperial College London
  • California Institute of Caltech (Caltech)
  • AWS Center for Quantum Computing
  • University of Copenhagen
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Details

Original languageEnglish
Pages (from-to)55-77
Number of pages23
JournalCommunications in Mathematical Physics
Volume385
Issue number1
Publication statusPublished - 10 Jun 2021
Externally publishedYes

Abstract

We extend quantum Stein’s lemma in asymmetric quantum hypothesis testing to composite null and alternative hypotheses. As our main result, we show that the asymptotic error exponent for testing convex combinations of quantum states ρ⊗n against convex combinations of quantum states σ⊗n can be written as a regularized quantum relative entropy formula. We prove that in general such a regularization is needed but also discuss various settings where our formula as well as extensions thereof become single-letter. This includes an operational interpretation of the relative entropy of coherence in terms of hypothesis testing. For our proof, we start from the composite Stein’s lemma for classical probability distributions and lift the result to the non-commutative setting by using elementary properties of quantum entropy. Finally, our findings also imply an improved recoverability lower bound on the conditional quantum mutual information in terms of the regularized quantum relative entropy—featuring an explicit and universal recovery map.

ASJC Scopus subject areas

Cite this

On Composite Quantum Hypothesis Testing. / Berta, Mario; Brandão, Fernando G.S.L.; Hirche, Christoph.
In: Communications in Mathematical Physics, Vol. 385, No. 1, 10.06.2021, p. 55-77.

Research output: Contribution to journal › Article › Research › peer review

Berta M, Brandão FGSL, Hirche C. On Composite Quantum Hypothesis Testing. Communications in Mathematical Physics. 2021 Jun 10;385(1):55-77. doi: 10.1007/s00220-021-04133-8
Berta, Mario ; Brandão, Fernando G.S.L. ; Hirche, Christoph. / On Composite Quantum Hypothesis Testing. In: Communications in Mathematical Physics. 2021 ; Vol. 385, No. 1. pp. 55-77.
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