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Experimental entropic uncertainty relations in dimensions three to five

Laura Serino1, Giovanni Chesi2, Benjamin Brecht1, Lorenzo Maccone2, Chiara Macchiavello2, and Christine Silberhorn1

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Phys. Rev. A 113, 032420 – Published 12 March, 2026

DOI: https://doi.org/10.1103/f6c4-jtlc

Abstract

We provide experimental validation of tight entropic uncertainty relations for the Shannon entropies of observables with mutually unbiased eigenstates in high dimensions. In particular, we address the cases of dimensions d=3, 4, and 5 and consider from 2 to d+1 mutually unbiased bases. The experiment is based on pulsed frequency bins measured with a multioutput quantum pulse gate, which can perform projective measurements on a complete high-dimensional basis in the time-frequency domain. Our results fit the theoretical predictions: the bound on the sum of the entropies is never violated and is saturated by the states that minimize the uncertainty relations.

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Phys. Rev. A 113, 032420– Published 12 March, 2026
  • Received 7 July 2025
  • Accepted 22 January 2026
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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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