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  • Letter
  • Open Access

Quantum state exclusion for group-generated ensembles of pure states

A. Diebra1,*, S. Llorens1, E. Bagan1, G. Sentís1,2, and R. Muñoz-Tapia1,3

  • 1Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
  • 2Ideaded, Carrer de la Tecnologia, 35, 08840 Viladecans, Barcelona, Spain
  • 3H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom

  • *Contact author: arnau.diebra@uab.cat
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Phys. Rev. Research 8, L012001 – Published 2 January, 2026

DOI: https://doi.org/10.1103/2k5d-bprn

Abstract

Quantum state exclusion is the task of determining which states from a given set a system was not prepared in. We provide a complete solution to optimal quantum state exclusion for arbitrary sets of pure states generated by finite groups, establishing necessary and sufficient conditions for perfect (zero-error conclusive) exclusion. When perfect exclusion is impossible, we introduce two natural extensions: minimum-error and unambiguous exclusion. For both, we derive the optimal protocols and present analytical expressions for the corresponding failure probabilities and measurements, providing additional insight into how quantum states encode information.

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Phys. Rev. Research 8, L012001– Published 2 January, 2026
  • Received 10 March 2025
  • Accepted 23 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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