Stephan Sponar and Ali Asadian
Photo Credit: Technische Universität Wien
Scientific Frontline: Extended "At a Glance" Summary: A New Uncertainty Relation for Quantum Measurement Errors
The Core Concept: A newly discovered mathematical formula in quantum physics that precisely quantifies the fundamental trade-off between the disturbance caused by an initial quantum measurement and the statistical correlation of a subsequent measurement.
Key Distinction/Mechanism: While the qualitative fact that quantum measurements disturb physical states has been known since Heisenberg, this new relation introduces an exact mathematical boundary. It states that the correlation squared plus the disturbance squared is always less than or equal to one, establishing a basic quantum trade-off analogous to wave-particle duality.
Major Frameworks/Components:
- Incompatible Observables: The foundational quantum principle that specific physical properties cannot be measured independently; observing one inevitably alters the state and affects subsequent measurements.
- Measurement Correlation: A statistical metric indicating how reliably the outcome of a secondary measurement can be predicted based on the results of the primary measurement.
- Measurement Disturbance: A quantitative value representing how severely an initial measurement intervenes in the particle's quantum state, thereby reducing correlation.
- Two-Level Systems (Qubits): The experimental framework involving neutron spins that the researchers used to physically test and confirm the theoretical inequality.
Branch of Science: Quantum Physics and Quantum Information Theory.
Future Application: The relation's symmetry provides a "self-calibration" feature that can be scaled for high-dimensional measurements of complex systems, making it highly useful for developing robust, semi-device-independent quantum communication protocols.
Why It Matters: This relation offers fundamentally new insights into quantum theory while providing scientists with an efficient, reliable, and precise tool to robustly estimate characteristic parameters of quantum measurement devices.
Researchers at TU Wien and IASBS have shown that the way different quantum measurements influence one another can be captured in a surprisingly simple formula.
One of the most striking features of quantum physics is that certain properties cannot be measured at the same time. Every measurement may inevitably affect 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.
Incompatible properties
“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.
Correlation and disturbance
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 showcases 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 correlation is 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.
Published in journal: Physical Review Research
Title: Covariant correlation-disturbance relation and its experimental realization with spin-1/2 particles
Authors: Ali Asadian, Florian Gams, and Stephan Sponar
Source/Credit: Technische Universität Wien
Reference Number: qs030326_01
.jpg)