One of the most striking features of quantum physics is that certain properties cannot be measured at the same time. Every measurement may inevitably affects the object’s physical state being measured – and therefore also the outcome of any subsequent measurement. How fast something is moving, for example, can depend on whether its position was measured beforehand.
How strongly a measurement intervenes in the quantum state determines how reliably the result of a second measurement can be predicted from the first. This qualitative connection has been known for a long time. What is new, however, is that researchers at TU Wien have now found a formula that allows this effect to be quantified exactly. They discovered a simple “uncertainty relation” that links measurement disturbance and measurement correlation. Using this relation, it becomes possible in a remarkably straightforward way to determine which combinations of quantum operations are possible – and which are fundamentally excluded.
“Measuring the weight of a car has no influence on its color,” explains Stephan Sponar from the Atominstitut at TU Wien. “Weight and color are completely independent physical properties. Measuring one does not affect the other.” In the quantum world, however, the situation is different. There are incompatible observables: measuring one of them inevitably influences the other. Werner Heisenberg already showed that position and momentum are not independent – the more precisely one is measured, the less precisely the other can be known. Similar effects arise when measuring the spin of a particle. If a particle is observed from above and one measures whether it rotates clockwise or counterclockwise, this intervenes in its spin state and influences the outcome of a subsequent measurement performed from a different direction.
“In practice, quantum measurements are never perfect,” says Florian Gams (TU Wien). “Measurement devices have imperfections; there are always inaccuracies and uncertainties.” This means that even if the same property is measured twice in succession, it is not guaranteed that the same result will always be obtained. There are also “gentle” measurements that disturb the quantum state only slightly – but in return do not provide a very reliable outcome.
Together with theoretical physicist Ali Asadian, who earned his PhD at Innsbruck University and now works at the Institute for Advanced Studies in Basic Sciences in Iran, Florian Gams and Stephan Sponar developed a theoretical model for such quantum measurements. In doing so, the team arrived at a remarkably simple relation: the correlation between two successive measurements is closely linked to the disturbance caused by the first measurement on the second one. Correlation squared plus disturbance squared is always smaller or equal to one. “The interplay between correlation and disturbance showcase a basic quantum trade-off relation reminiscent of wave-particle duality ,” says Ali Asadian.
Correlation is a measure of how well the outcome of a second measurement can be inferred from the first. In some cases, the first measurement tells us nothing about the second (fully uncorrelated). On the other hand, when two similar measurements are performed, there is a statistical correlation between the two outcomes.
The “disturbance” quantifies how strongly a measurement intervenes in the particle’s state – that is, how much the correlationis reduced by the measurement process.
The newly discovered relation was tested at TU Wien using neutron spins, a so-called two-level system or short qubit . The team performed spin measurements in different directions, sometimes with a stronger, sometimes with a weaker intervention in the neutron’s quantum state. “The results agree extremely well with our inequality,” says Stephan Sponar. “Our theory predicts that if correlation and disturbance are determined and plotted in a plane, all values must lie on a circle in the optimal case – and that is exactly what we observe in our measurements.
This symmetry property provides an efficient tool for robust experimental estimation of characteristic parameters (e.g. measurement strength) of quantum measurement devices. It is important to mention, that this procedure can also be applied in high-dimensional measurements of more complex systems, allowing for applications of this “self-calibration” feature for instance in (semi) device-independent quantum communication protocols.
The surprisingly simple relation does not only constitute a fundamentally new insight into quantum theory itself. It also provides a new way to characterize and witness resourceful quantum measurements in a simple, reliable, and precise manner.
Physical Review Research
Experimental study
Not applicable
Covariant correlation-disturbance relation and its experimental realization with spin-1/2 particles
13-Jan-2026