Heisenberg's error-disturbance relation proved correct

One of the basic concepts in quantum mechanics is that it is impossible to observe physical objects without affecting them in a significant way; there can be no measurement without disturbance. In 1927, theoretical physicist Werner Heisenberg claimed that this fact could be expressed as an uncertainty relation, describing a reciprocal relation between the accuracy in position and the disturbance in momentum.

Heisenberg’s theory was largely based on intuition, with no evidence provided. Now over 80 years later, an international team of scientists has published such evidence in the journal Physical Review Letters. Their research was funded by the Academy of Finland; the European Network Simulators and Interfaces with Quantum Systems (SIQS); and COST (European Cooperation in Science and Technology).

Professor Paul Busch of the University of York, Professor Pekka Lahti of the University of Turku and Professor Reinhard Werner of Leibniz Universität Hannover have provided a precise formulation and proof of the error-disturbance relation. Their work has implications for the developing field of quantum cryptography and computing, as it reaffirms that quantum-encrypted messages can be transmitted securely since an eavesdropper would necessarily disturb the system carrying the message and this could be detected.

Professor Busch said: “While the slogan ‘no measurement without disturbance’ has established itself under the name ‘Heisenberg effect’ in the consciousness of the scientifically interested public, a precise statement of this fundamental feature of the quantum world has remained elusive, and serious attempts at rigorous formulations of it as a consequence of quantum theory have led to seemingly conflicting preliminary results.”

The scientists considered how simultaneous measurements of a particle’s position and momentum are calibrated. They defined the errors in these measurements as the spreads in the distributions of the outcomes in situations where either the position or the momentum of the particle is well defined. They found that these errors for combined position and momentum measurements obey Heisenberg’s principle.

“Despite recent claims to the contrary, Heisenberg-type inequalities can be proven that describe a trade-off between the precision of a position measurement and the necessary resulting disturbance of momentum and vice versa,” said Professor Busch.

Professor Werner added: “Since I was a student I have been wondering what could be meant by an ‘uncontrollable’ disturbance of momentum in Heisenberg’s Gedanken experiment. In our theorem this is now clear: not only does the momentum change, there is also no way to retrieve it from the post-measurement state.”

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