Suppose that one could "flip" a coin, and that it settled onto a platform. For simplicity, let the coin processed with the nonzero angular momentum on $y$ axis only. To further simplify the question, suppose that the platform was in vacuum, and the "falling" of the coin onto the platform was created by some "fictional force", that act with a potential of $1/r$.
It's obvious that the process were all unitary (reversible) since it's "classical". However, once the coin settled onto the platform with the dissipation of the (kinetic) energy, it's evidential that one could not determine the states for which it came from.
Thus, one had a "measurement" for which the entire process was unitary. This seemed to be some what counter intuitive to the usual non relativistic quantum mechanics, as a measurement was somewhat "magical". How was a "measurement" being "unitary"? How could one ever settle with a coin flip?