1306.1565 (Paul Busch et al.)

Proof of Heisenberg's error-disturbance relation    [PDF]

Paul Busch, Pekka Lahti, Reinhard F. Werner

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. Here we show that despite recent claims to the contrary [Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)], 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). More generally, these inequalities are instances of an uncertainty relation for the imprecisions of any joint measurement of position and momentum.

View original: http://arxiv.org/abs/1306.1565