1. Every random-number-generator has a coherence-length. This means, after maybe a billion turns exactly the same numbers will start popping up again in exactly the same sequence. There are mathematical/computational tricks to increase the coherence-length of a random-number-generator, but you will never get a perfect chaos. That's why random numbers created by a computer are considered "pseudo-random numbers".
2. Quantum-mechanics allows such a perfect chaos, because it considers matter being in several states at the same time, each one with the same probability. Only measurement (be it by a sentient being or by just another particle nearby) determines the state. There is no way to predict future behavior with absolute certainty.
If you make the system big enough, the quantum-nature becomes more and more irrelevant and predictability arises.
3. Consider a box with nothing in it. Absolutely nothing. If you calculate the electromagnetic field inside the box, you will get a quantized solution, showing that there is no electromagnetic field, ON AVERAGE. The mean amplitude of the electromagnetic waves is zero, but probability distributions consist of more parameters than just the mean (an infinite number of parameters, just like the parameters in a Taylor expansion). The standard deviation of the electromagnetic field is not zero.
This means, there are fluctuations inside your empty box, but the overall mean is always perfectly zero. These fluctuations are described as virtual photons, which appear at random, have a random direction, and disappear at random.
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