> Randomness is not only found in quantum mechanics; classical mechanics
> contains plenty of randomness, e.g. in a perfect gas, brownian movement,
> or thermal fluctuations, or even radio static... But classical noise
> tends to be more "analog" and therefore harder to calibrate, while
> quantum mechanics lends itself better to digitization.
Classical mechanics is by definition a deterministic theory (irreversibility only comes into play with statistical mechanics, which is an effective approximation of classical mechanics for very large systems), and strictly speaking, no randomness can be gained in this framework at all. Systems may /seem/ random, but this randomness is only epistemological, caused by insufficient knowledge about the (initial conditions of the) system. Quantum mechanics, on the other hand, is able to describe ontological randomness. This is not influenced by the dimension of the Hilbert space under consideration, which roughly translates into "analog" or "discrete" systems: A finite-dimensional quantum system can contain randomness that stems exclusively from the mixedness of the state, and an infinite-dimensional quantum system can be a perfect provider of randomness (the vacuum state of an electromagnetic field is one particularly convenient possibility, for instance).
Since the measurement process is invariably classical in nature with current-day technology, it is also impossible to produce perfect randomness even with perfect quantum systems -- the measurement noise will always influence the result. However, there are fortunately means of distilling nearly perfect randomness given knowledge about the entropy (or, to be precise, the conditional min-entropy) of the measured state, given some initial amount of nearly perfect randomness as seed.