All sets of incompatible measurements give an advantage in quantum state discrimination

Paul Skrzypczyk, Ivan Supic, Daniel Cavalcanti

Research output: Contribution to journalArticle (Academic Journal)peer-review

34 Citations (Scopus)
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Some quantum measurements cannot be performed simultaneously; i.e., they are incompatible. Here we show that every set of incompatible measurements provides an advantage over compatible ones in a suitably chosen quantum state discrimination task. This is proven by showing that the robustness of incompatibility, a quantifier of how much noise a set of measurements tolerates before becoming compatible, has an operational interpretation as the advantage in an optimally chosen discrimination task. We also show that if we take a resource-theory perspective of measurement incompatibility, then the guessing probability in discrimination tasks of this type forms a complete set of monotones that completely characterize the partial order in the resource theory. Finally, we make use of previously known relations between measurement incompatibility and Einstein-Podolsky-Rosen steering to also relate the latter with quantum state discrimination.
Original languageEnglish
Article number130403
Number of pages6
JournalPhysical Review Letters
Issue number13
Publication statusPublished - 2 Apr 2019

Structured keywords

  • QITG
  • Bristol Quantum Information Institute


  • quantum measurements
  • quantum nonlocality
  • resource theories


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