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Universality in fidelity-based quantum metrology

Luis Aragón-Muñoz1,*, Chryssomalis Chryssomalakos1,†, Ana Gabriela Flores-Delgado1,‡, John Martin2,§, and Eduardo Serrano-Ensástiga2,∥

  • 1Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, PO Box 70-543, 04510 Ciudad de México, México
  • 2Institut de Physique Nucléaire, Atomique et de Spectroscopie, CESAM, University of Liège, B-4000 Liège, Belgium

  • *Contact author: luis.aragon@correo.nucleares.unam.mx
  • †Contact author: chryss@nucleares.unam.mx
  • ‡Contact author: ana.flores@correo.nucleares.unam.mx
  • §Contact author: jmartin@uliege.be
  • ∥Contact author: ed.ensastiga@uliege.be
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Phys. Rev. A 114, 032406 – Published 3 September, 2026

DOI: https://doi.org/10.1103/gpp5-n5j6

Abstract

We consider the problem of identifying the quantum spin states that are the optimal sensors of a given transformation, averaged over all possible orientations of the spin system. Our geometric approach to the problem is based on a fidelity criterion and is entirely general, encompassing any unitary transformation. This formalism leads to a universality result: For any value of the spin, there exists a zero-measure subset of states that can be the optimal sensors for certain transformations and the worst sensors for others, and this set does not depend on the transformation under consideration. In other words, some spin states are simply the best (or worst) sensors, regardless of what they detect.

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Outline

Information

Phys. Rev. A 114, 032406– Published 3 September, 2026
  • Received 7 October 2025
  • Revised 15 June 2026
  • Accepted 21 July 2026
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