The Semiring of Dichotomies and Asymptotic Relative Submajorization

Christopher Perry, Peter Vrana*, Albert H. Werner

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

4 Citations (Scopus)

Abstract

We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassen's theorem on preordered semirings. We find that an asymptotic variant of relative submajorization, defined on unnormalized dichotomies, is characterized by real-valued monotones that are multiplicative under the tensor product and additive under the direct sum. These strong constraints allow us to classify and explicitly describe all such monotones, leading to a rate formula expressed as an optimization involving sandwiched Renyi divergences. As an application we give a new derivation of the strong converse error exponent in quantum hypothesis testing.

Original languageEnglish
JournalIEEE Transactions on Information Theory
Volume68
Issue number1
Pages (from-to)311-321
Number of pages11
ISSN0018-9448
DOIs
Publication statusPublished - 1 Jan 2022

Keywords

  • Testing
  • Tensors
  • Entropy
  • Technological innovation
  • Quantum channels
  • Optimization
  • Information theory
  • Relative submajorization
  • quantum resource theory
  • sandwiched Renyi divergence
  • strong converse exponent
  • QUANTUM
  • SPECTRUM

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