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  • Open Access

Robust Certification of Non-Projective Measurements: Theory and Experiment

Raphael Brinster1,*, Peter Tirler2,*, Shishir Khandelwal3, Michael Meth2, Hermann Kampermann1, Dagmar Bruß1, Rainer Blatt2,4, Martin Ringbauer2, Armin Tavakoli3 et al.

Nikolai Wyderka1

  • *These authors contributed equally to this work.
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PRX Quantum 7, 033005 – Published 6 July, 2026

DOI: https://doi.org/10.1103/nsjr-vnmg

Abstract

Determining the conditions under which positive operator-valued measures (POVMs), the most general class of quantum measurements, outperform projective measurements remains a challenging and largely unresolved problem. Of particular interest are projectively simulable POVMs, which can be realized through probabilistic mixtures of projective measurements and therefore offer no advantage over projective schemes. Characterizing the boundary between simulable and non-simulable POVMs is, however, a difficult task, and existing tools either fail to scale efficiently, provide limited experimental feasibility, or work only for specific POVMs. Here, we introduce and demonstrate a general method to certify non-simulability of a POVM by introducing a complete hierarchy of semidefinite programs. It provides upper bounds on the non-simulability measure of critical visibility of arbitrary POVMs, which are tight in many cases and outperform previously known criteria. We experimentally certify the non-simulability of two- and three-dimensional POVMs using a trapped-ion qudit quantum processor by constructing non-simulability witnesses and introducing a modification of our framework that makes them robust against state preparation errors. Finally, we extend our results to the setting where an additional ancilla system is available.

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Popular Summary

Quantum technology has advanced to a point where moving beyond textbook projective measurements has become a practical reality. Generalized measurements, so-called “positive operator-valued measures” or “POVMs” promise to enhance quantum information processing in a wide range of areas. Yet, many POVMs can be simulated, which means the exact same result can be achieved using multiple projective measurements instead. In this work, we developed a simple technique to certify whether any given POVM can be simulated in such a way or not. We demonstrated this technique by certifying the non-simulability of two fundamentally different POVMs on a trapped-ion quantum computer. Identifying non-simulable POVMs is not only important for the practical advantages many offer, but in contexts like certification or security proofs, it becomes non-negotiable. Therefore, the certification protocol presented in this work is a key ingredient to a wider use of POVMs in mainstream applications.

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PRX Quantum 7, 033005– Published 6 July, 2026
  • Received 14 November 2025
  • Accepted 21 May 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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