Heisenberg uncertainty for qubit measurements

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, we have presented and proven a Heisenberg-type relation for joint measurements of position and momentum [Phys. Rev. Lett. 111, 160405 (2013)]. To resolve the apparent conflict, we formulate here a new general trade-off relation for errors in qubit measurements, using the same concepts as we did in the position-momentum case. We show that the combined errors in an approximate joint measurement of a pair of +/-1 valued observables A,B are tightly bounded from below by a quantity that measures the degree of incompatibility of A and B. The claim of a violation of Heisenberg is shown to fail as it is based on unsuitable measures of error and disturbance. Finally we show how the experiments mentioned may directly be used to test our error inequality.Comment: Version 3 contains further clarifications in our argument refuting the alleged violation of Heisenberg's error-disturbance relation. Some new material added on the connection between preparation uncertainty and approximation error relation

Transport, atom blockade and output coupling in a Tonks-Girardeau gas

Recent experiments have demonstrated how quantum-mechanical impurities can be created within strongly correlated quantum gases and used to probe the coherence properties of these systems [S. Palzer, C. Zipkes, C. Sias, and M. K\"ohl, Phys. Rev. Lett. 103, 150601 (2009).]. Here we present a phenomenological model to simulate such an output coupler for a Tonks-Girardeau gas that shows qualitative agreement with the experimental results for atom transport and output coupling. Our model allows us to explore nonequilibrium transport phenomena in ultracold quantum gases and leads us to predict a regime of atom blockade, where the impurity component becomes localized in the parent cloud despite the presence of gravity. We show that this provides a stable mixed-species quantum gas in the strongly correlated limit