  We use the classical correlation between a quantum system being measured and
its measurement apparatus to analyze the amount of information being retrieved
in a quantum measurement process. Accounting for decoherence of the apparatus,
we show that these correlations may have a sudden transition from a decay
regime to a constant level. This transition characterizes a non-asymptotic
emergence of the pointer basis, while the system-apparatus can still be quantum
correlated. We provide a formalization of the concept of emergence of a pointer
basis in an apparatus subject to decoherence. This contrast of the pointer
basis emergence to the quantum to classical transition is demonstrated in an
experiment with polarization entangled photon pairs.
