Experimental Demonstration of a generalized Error-Disturbance Uncertainty Relation

Heisenberg’s uncertainty principle is certainly one of the most famous foundations of quantum physics. According to this principle, not all properties of a quantum particle are determined with arbitrary accuracy. In the early days of quantum theory, this has often been justified by the notion that every measurement inevitably recoils the quantum particle, which disturbs the results of any further measurements. This, however, turns out to be an oversimplification. In our neutron optical experiment different sources of quantum uncertainty could now be distinguished, validating theoretical results our  from Japanese collaborator theoretical physicist Masanao Ozawa. The influence of the measurement on the quantum system is only one reason for the uncertainty observed in the experiment. Heisenberg’s arguments for the uncertainty principle have to be revisited – the uncertainty principle itself however remains valid. Our results have now been published in the journal Nature Physics ¹.

The effect of the measurement on the quantum system and the resulting disturbance of the second measurement is not the core of the problem. The uncertainty is rooted in the quantum nature of the particle. Quantum particles cannot be described like a point-like object with a well-defined velocity. Instead, quantum particles behave as a wave – and for a wave, position and momentum cannot be defined accurately at the same time. In order to describe the fundamental uncertainty and the additional disturbance due to the measuring process, both particle and measurement device have to be treated in the framework of quantum theory as done by the Japanese physics Masanao Ozawa in 2003, leading to a generalized uncertainty principle (see here for details). His equations contain different “kinds of uncertainty”: On the one hand the uncertainty which comes from the measurement, as it disturbs the particle, on the other hand the equations contain the fundamental quantum uncertainty, which is present in any quantum system, regardless of the measurement. Instead of a particle’s position and momentum, the spin of neutrons is measured in our experiment. A schematic illustration of our setup is depicted aside. The neutron polarimetric can ban be seen here:

Neutron polarimetric setup for testing error-disturbance uncertainty relations in successive neutron spin measurements. The setup is divided in four stages: state preparation, apparatus A1 carrying out the x-measurement. Apparatus A2 performs a subsequent measurement of spin’s y-component (the correction operation is not applied in the first experiments).

The spin in -direction and the spin in -direction cannot be measured simultaneously: they fulfill the uncertainty relation, in much the same way as position and momentum. To demonstrate the generalized uncertainty relation, an apparatus consisting of three stages has been designed.  In the first step, the neutron’s spin state is prepared. Then, measurements of the – and -component of the spin are performed successively on every incoming neutron.  An error in the first measurement therefore unavoidably disturbs the second measurement. This effect adds up to the fundamental uncertainty stemming from the quantum nature of the neutron. Preparation and measurement of the neutron’s spin is achieved by exploiting appropriately oriented static magnetic fields together with polarizing super mirrors. Now a systematic investigation of the trade-off between error and disturbance  is performed. Instead of a precise measurement of  in –direction, which would disturb a posterior -measurement in y-direction maximally, an approximate measurement of , referred to as , with a deviation angle , being the azimuthal angle on the equatorial plane of the Bloch-sphere, is performed. Error and disturbance are determined from detected count rates (see here for details) of the successive measurements as plotted here. What has been finally observed is the fact that all pairs of error and disturbances (yellow) are located below the bound defined by a naive Heisenberg error-disturbance relation, but reproduce the predictions of Ozawa’s new relation. In summary, we have demonstrated experimental validity of Ozawa’s universally valid error-disturbance uncertainty relation in a neutron polarimetric experiment. The theoretical predictions are reproduced evidently at a high degree of accuracy.

Press Relase TU Wien (see here for german version)

1. J. Erhart, S. Sponar, G. Sulyok, G.Badurek, M. Ozawa, and Y. Hasegawa Nature Physics 8, 185-189 (2012)
[quant-ph/1201.1833].↩

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