Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. The noise is often thought to come from the measurements' failure to commute. However, not all measurements are projective. In particular, weak measurements are minimally invasive tools for obtaining partial state information without projection.
In this talk, I'll describe an experiment in which such measurements can reconcile two incompatible (non-commuting) strong measurements. The weak measurements' slight back action on the state accounts for a majority of the reconciliation. The measurements obey an entropic uncertainty relation based on generalized measurement operators. In this relation a weak value appears, lowering the uncertainty bound.
[Monroe et al. PRL 126, 100403 (2021)]