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  • Open Access

Weak convexity of Fisher information matrix and superresolved localization of blinking sources of light

Dmitri B. Horoshko1,*, Alexander B. Mikhalychev2, Fedor Jelezko1, and Polina P. Kuzhir3

  • *Contact author: dmitri.horoshko@uni-ulm.de
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Phys. Rev. Research 7, 033065 – Published 17 July, 2025

DOI: https://doi.org/10.1103/t48h-6hcf

Abstract

A group of techniques known by the general name of single-molecule localization microscopy reaches a nanometer-scale spatial resolution of point light emitters, well below the diffraction limit of traditional microscopy. The key feature of these techniques is blinking, alternation of bright and dark states, of each emitter so that no more than one emitter is bright within the width of the point-spread function of the microscope during a time sufficient for its localization. We give a formulation of the optical part of these techniques in terms of quantum metrology, where the limit of precision is determined by the Fisher information on the emitters' positions contained in the measurement data. We show that the advantage in resolution provided by making the emitters blink is a consequence of the fundamental property of Fisher information, its convexity. In particular, we prove the weak matrix convexity and the trace convexity of the Fisher information matrix—two fundamental results in the multiparameter estimation theory. We show also that the advantage in information is inherent to the quantum state of light itself before the measurement and is related to the convexity of the quantum Fisher information matrix.

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Phys. Rev. Research 7, 033065– Published 17 July, 2025
  • Received 4 February 2025
  • Accepted 11 June 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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