Proving that one quantum measurement is more powerful than another has long been difficult. Physicists from Heinrich Heine University Düsseldorf, Lund University, and the University of Innsbruck have now developed and demonstrated a simple technique to certify that a certain class of measurements has properties that cannot be mimicked by simpler means.
Measurements are central to all quantum technologies. They are said to 'collapse' the quantum state they act on, destroying its quantum properties and serving as the bridge to the classical world. Curiously, quantum mechanics allows for measurements that are more general than the ones we can directly associate with classical properties of a system.
These generalized measurements, or POVMs, short for Positive Operator Valued Measures, are not just a mathematical curiosity. They are known to improve performance in tasks like distinguishing between quantum states that would otherwise be indistinguishable, extracting more information from quantum sensors, and securing quantum communication. Yet POVMs are difficult to realize in an actual quantum device, and it is often hard to prove that they truly outperform simpler measurements, making it hard to know whether their added complexity is worth it. This new certification method gives researchers a practical tool to answer that question.
Certifying POVMs that cannot be simulated
"While some POVMs genuinely offer more than standard measurements, others can be 'simulated' using simpler means, such as collections of standard measurements," explains Raphael Brinster from the University of Düsseldorf. Identifying POVMs that cannot be 'simulated' by processing standard measurements is therefore key to understanding the benefits of generalized measurements and unlocking their use in quantum devices. Until now, however, guaranteeing that no such simulation exists has been a major challenge.
The collaboration between Düsseldorf, Lund, and Innsbruck has developed and demonstrated an algorithm that provides this certification efficiently, using only a small set of measurements. The resulting certificate guarantees that no combination of standard measurements could reproduce the POVM's results. Crucially, the certification is not just a theoretical result: it is robust enough to withstand real experimental imperfections, as the team showed by certifying non-simulable measurements on a quantum computer in Innsbruck.
Made possible by a new paradigm in quantum computing
Realizing POVMs on a quantum computer is difficult in practice, since they can have more outcomes than the two a single qubit can produce. Implementing such measurements and certifying them was only made possible by a novel quantum computing platform developed at the University of Innsbruck, one that moves beyond binary qubits to work with logic of arbitrary dimension.
These so-called "qudits" not only promise more efficient quantum information processing, but also unlock techniques unavailable with qubits alone. "These results demonstrate that the use of qudits, even just to aid measurements, can greatly increase the utility of quantum technologies," says Martin Ringbauer , who leads the Innsbruck team.
The research was financially supported, among others, by the Austrian Science Fund (FWF), the Federal Ministry of Education, Science and Research, the Austrian Research Promotion Agency (FFG), the European Union, the Swedish Research Council, and the German Research Foundation (DFG).
Publication: Robust Certification of Non-Projective Measurements: Theory and Experiment. Raphael Brinster, Peter Tirler, Sishir Khandelwal, Michael Meth, Hermann Kampermann, Dagmar Bruß, Rainer Blatt, Martin Ringbauer, Armin Tavakoli & Nikolai Wyderka. PRX Quantum (2026) DOI: 10.1103/nsjr-vnmg [arXiv: 2511.04446 ]
