The answer to 2) depends on how disturbance is understood, particularly since measurement entails disturbance (however note that this is the observer effect, which is distinct from the uncertainty principle). Still, in the most natural interpretation the answer is also no. To see this, consider two sequences of measurements: (A) that measures exclusively σ 1 and (B) that measures only σ 3 of a spin system in the state ψ. The measurement outcomes of (A) are all +1, while the statistical distribution of the measurements (B) is still divided between +1, −1 with equal probability.