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  • Open Access

Fundamental limits on determination of photon number statistics from measurements with multiplexed on/off detectors

Jaromír Fiurášek*

  • Department of Optics, Faculty of Science, Palacký University, 17. listopadu 12, 77900 Olomouc, Czech Republic

  • *Contact author: fiurasek@optics.upol.cz
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Phys. Rev. Research 7, 033147 – Published 13 August, 2025

DOI: https://doi.org/10.1103/49wr-wgf7

Abstract

We investigate fundamental bounds on the ability to determine photon number distribution and other related quantities from tomographically incomplete measurements with an array of M detectors that can only distinguish the absence or presence of photons. We show that the lower and upper bounds on photon number probabilities can be determined by solving a linear program. We present and discuss numerical results for various input states, including thermal states, coherent states, squeezed states, and highly nonclassical single-photon subtracted squeezed vacuum states. Besides photon number probabilities, we also investigate bounds on the parity of photon number distribution that determines the value of Wigner function of the state at the origin of phase space. Moreover, we also discuss estimation of mean photon number as an example of a quantity described by an unbounded operator. Our approach and results can provide quantitative guidance on the number of detection channels required to determine the photon number distribution with a given precision.

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Phys. Rev. Research 7, 033147– Published 13 August, 2025
  • Received 27 March 2025
  • Accepted 23 July 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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