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  • Open Access

Multiobject operational tasks for measurement incompatibility

Andrés F. Ducuara1,2,*,†, Ryo Takakura3,4,‡, Fernando J. Hernandez5, and Cristian E. Susa5

  • *Present address: Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore.
  • †Contact author: andres.dg@ntu.edu.sg
  • ‡Contact author: takakura.ryo.qiqb@osaka-u.ac.jp
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Phys. Rev. Research 7, 033050 – Published 11 July, 2025

DOI: https://doi.org/10.1103/m7ln-tb1s

Abstract

We introduce multiobject operational tasks for measurement incompatibility in the form of multiobject quantum subchannel discrimination and exclusion games with prior information, where a player can simultaneously harness the resources contained within both a quantum state and a set of measurements. We show that any fully or partially resourceful pair of objects is useful for a suitably chosen multiobject subchannel discrimination and exclusion game with prior information. The advantage provided by a fully or partially resourceful object against all possible fully free objects in such a game can be quantified in a multiplicative manner by the resource quantifiers of generalized robustness and the weight of a resource for discrimination and exclusion games, respectively. These results hold for arbitrary properties of quantum states as well as for arbitrary properties of sets of measurements closed under classical pre- and postprocessing and, consequently, include measurement incompatibility as a particular case. We furthermore show that these results are not exclusive to quantum theory, but can also be extended to the realm of general probabilistic theories.

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Phys. Rev. Research 7, 033050– Published 11 July, 2025
  • Received 7 January 2025
  • Accepted 9 June 2025
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