It has long been challenging to demonstrate the superiority of one quantum measurement over another. Physicists from the University of Innsbruck, Lund University, and Heinrich Heine University Düsseldorf have now developed and shown a simple method to guarantee that a certain class of measurements has properties that cannot be replicated by simpler techniques. PRX Quantum reported the findings.
Ion-trap processors are among the most advanced and successful platforms in quantum technology. Part of it is this setup at the University of Innsbruck. Image Credit: University of Innsbruck
All quantum technologies rely on measurements. When a quantum state is measured, it is said to “collapse,” losing its quantum properties and becoming a bridge to the classical world. Remarkably, quantum mechanics also makes it possible to perform measurements that extend beyond those directly associated with a system’s classical attributes.
Positive Operator Valued Measures, or POVMs for short, are generalized measurements that are more than simply a mathematical curiosity. They are known to enhance performance in tasks such as safeguarding quantum communication, obtaining additional information from quantum sensors, and differentiating between quantum states that would otherwise be indistinguishable.
However, POVMs are challenging to implement on real quantum devices, and demonstrating their superiority over simpler measurement strategies is often difficult. As a result, it has been unclear whether their added complexity is justified. This new certification process provides researchers with a valuable tool for addressing 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.
Raphael Brinster, University of Düsseldorf
Realizing the benefits of generalized measurements and enabling their use in quantum devices depends on identifying POVMs that cannot be “simulated” by processing standard measurements. Until now, however, proving that no such simulation is possible has remained a major challenge.
Researchers from Innsbruck, Lund, and Düsseldorf have now developed and demonstrated an algorithm that efficiently provides this certification using only a limited number of measurements. The resulting certificate guarantees that the outcomes produced by the POVM cannot be reproduced by any combination of standard measurements.
Crucially, the certification is not merely a theoretical result: it can endure real-world experimental defects, as demonstrated by the team’s certification of non-simulable measurements on a quantum computer in Innsbruck.
Made Possible by a New Paradigm in Quantum Computing
POVMs are challenging to implement on quantum computers because they can produce more than two possible outcomes. Implementing and validating these measurements became feasible only with a novel quantum computing platform developed at the University of Innsbruck. Unlike conventional binary qubits, the platform operates with logic of arbitrary dimensions.
These higher-dimensional quantum systems, known as “qudits,” not only enable more efficient quantum information processing but also support measurement and computation techniques that are not possible with qubits alone.
These results demonstrate that the use of qudits, even just to aid measurements, can greatly increase the utility of quantum technologies.
Martin Ringbauer, Assistant Professor, University of Innsbruck
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) all provided financial support for the research.
Journal Reference:
Brinster, R., et al. (2026) Robust Certification of Non-Projective Measurements: Theory and Experiment. PRX Quantum. DOI: 10.1103/nsjr-vnmg. https://journals.aps.org/prxquantum/abstract/10.1103/nsjr-vnmg.