Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin measurements

Abstract

The uncertainty principle generally prohibits simultaneous measurements of certain pairs of observables and forms the basis of indeterminacy in quantum mechanics 1. Heisenberg's original formulation, illustrated by the famous γ-ray microscope, sets a lower bound for the product of the measurement error and the disturbance 2. Later, the uncertainty relation was reformulated in terms of standard deviations 3-5, where the focus was exclusively on the indeterminacy of predictions, whereas the unavoidable recoil in measuring devices has been ignored 6. A correct formulation of the error-disturbance uncertainty relation, taking recoil into account, is essential for a deeper understanding of the uncertainty principle, as Heisenberg's original relation is valid only under specific circumstances 7-10. A new error-disturbance relation, derived using the theory of general quantum measurements, has been claimed to be universally valid 11-14. Here, we report a neutron-optical experiment that records the error of a spin-component measurement as well as the disturbance caused on another spin-component. The results confirm that both error and disturbance obey the new relation but violate the old one in a wide range of an experimental parameter. © 2012 Macmillan Publishers Limited. All rights reserved.