state is therefore called an *eigenstate* (also “basis state"). One says that the initial state of the quantum system has *collapsed* into, or been *reduced* to, an eigenstate as the result of the first intervention. In other words, after the measurement the quantum system behaves “classically” *with respect to the variable in question*.

Sometimes, the same apparatus can be used in different configurations (e.g., rotation of a Stern-Gerlach set-up or a polarization filter); experiments show that each configuration may have a different set of basis states. In other cases there are no alternatives for the same instrumental setup (for instance, the “which-path” observable in a Mach-Zehnder interferometer; the wavelength of a spectral emission; the decay products of a particle); the eigenstates are then called “preferred basis states”. On the other hand, one single quantum system may have more than one observable to measure (several degrees of freedom like the position, momentum and spin vectors of a particle); in that case, the measurement results of one observable may or may not affect (be correlated with) the distribution of measurement results of another. This means that having many multi-degree of freedom quantum systems prepared in identical ways, making the measurement of one 