Can you show an actual error if such an association is made?Again! A particle is not (and in no picture of time evolution whatsoever) a Hilbert-space vector and its observables are no self-adjoint operators on the Hilbert space. There are real things in the lab called measurement apparati and a particle source but no mathematical abstract objects. The link to associate the mathematical abstract objects of the theory and the real-world equipment is Born's Rule, associating the modulus squared of a wave function with the probabilities and/or probability densities of the occurance of measurement results, and these probailities (and derived quantities from them like expectation values of observables or scattering cross sections and the like) are independent of the picture chosen. Any attempt to associate real-world equipment directly with the abstract objects of the QT formalism leads to confusion and are thus of no help!