Weak Measurements of a Superconducting Qubit Reconcile Incompatible Observables

Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. The noise comes from the observables' not sharing an eigenbasis. However, not all measurements are projective. In particular, weak measurements are minimally invasive tools for obtaining partial state information without projection. Weak measurements obey an entropic uncertainty relation based on generalized measurement operators [Yunger Halpern et al. Commun. Phys. 2, 92 (2019)]. We experimentally test the entropic uncertainty relation with strong and weak measurements of a superconducting transmon qubit. We find that a weak measurement can reconcile the incompatibility of two strong measurements via the weak measurement's backaction.