Quantum rms error and Heisenberg's error-disturbance relation

Paul Busch, S. Varró, P. Ádám, T.S. Biró, G.G. Barnaföldi, P. Lévai
2014 EPJ Web of Conferences  
Reports on experiments recently performed in Vienna [Erhard et al, Nature Phys. 8, 185 (2012)] and Toronto [Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)] include claims of a violation of Heisenberg's error-disturbance relation. In contrast, a Heisenberg-type tradeoff relation for joint measurements of position and momentum has been formulated and proven in [Phys. Rev. Lett. 111, 160405 (2013)]. Here I show how the apparent conflict is resolved by a careful consideration of the quantum
more » ... alisation of the notion of root-mean-square error. The claim of a violation of Heisenberg's principle is untenable as it is based on a historically wrong attribution of an incorrect relation to Heisenberg, which is in fact trivially violated. We review a new general trade-off relation for the necessary errors in approximate joint measurements of incompatible qubit observables that is in the spirit of Heisenberg's intuitions. The experiments mentioned may directly be used to test this new error inequality.
doi:10.1051/epjconf/20147801002 fatcat:snpgol2ujvgg7mjp5gdl75g37q