Optimal observables for minimum-error state discrimination in general probabilistic theories

Koji Nuida, Gen Kimura, Takayuki Miyadera

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

General probabilistic theories provide the most general mathematical framework for the theory of probability in an operationally natural manner and generalize classical and quantum theories. In this article, we study state discrimination problems in general probabilistic theories using a Bayesian strategy. After reformulation of the theories with mathematical rigor, we first prove that an optimal observable to discriminate any (finite) number of states always exists in the most general setting. Next, we revisit our recently proposed geometric approach for the problem and show that for two-state discrimination, this approach is indeed effective in arbitrary dimensional cases. Moreover, our method reveals an operational meaning of Gudder's "intrinsic metric" by means of the optimal success probability, which turns out to be a generalization of the trace distance for quantum systems. As its by-product, an information disturbance theorem in general probabilistic theories is derived, generalizing its well known quantum version.

Original languageEnglish
Article number093505
JournalJournal of Mathematical Physics
Volume51
Issue number9
DOIs
Publication statusPublished - 2010 Sep 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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