where Δ Δ a = ⟨ ⟨ a ^ ^ 2 ⟩ ⟩ − − ⟨ ⟨ a ^ ^ ⟩ ⟩ 2 is a standard deviation of observable a and ⟨ ⟨ a ^ ^ ⟩ ⟩ stands for expectation value of a in whatever quantum state the system is. The equality is reached if the system is in a minimum uncertainty state. The consequence for our case is that the more precise is our measurement, i.e the smaller is Δ Δ δ δ O , the larger will be perturbation the Meter exerts on the measured observable x ^ ^ . Therefore, the readout of the meter will, in general, consist of three terms: