Consider everyone's favourite pseudo random number generator, RANDU where V is the output of any successive iteration.
$$ V_{j+1} = 65539 \cdot V_j \; mod \; 2^{31} $$
I've purposefully chosen RANDU because it's not so good a PRNG, but works well in my example. Such linear congruential generators can be easily inverted to recover the state, and hence predict all future values.
Now let's replace the 65539 constant with a normal probability distribution, A. And let's define A as:-
A = NORMAL(μ =~ 65538.5, σ =~ 998) where the values are rough approximations obtained by mysterious empirical means. An integer rounding operation happens somewhere. It's my cunning model of a diode that might be used for an entropy source inside a TRNG. A represents the Avalanche Effect inside certain diodes, and looks like a children's Galton board as electrons tumble through the semiconductor material.
Lastly, assume we have a mega quantum computer slurping up all the output from this random generator. Are we able to predict the future output, given enough samples? And if not, can we say anything at all about the security of this generator? Would it now be a true unpredictable entropy source, or would we able to get almost perfect estimates of the future output sequence?
This is a highly theoretical question, but I'm trying to get a perspective on what may /may not be possible in derandomising entropy sources given quantum computers. I emphasise derandomising, as this and equivalent terms have previously been used in discussions of classical entropy sources for true random number generation. There is a long list of Similar Questions on my screen suggesting the upcoming end of traditional randomness. Some will posit that if the quantum computer can form sufficient simultaneous equations, it can determine the internal state of the diode via ersatz linear cryptanalysis. This is my attempt at countering.
Even some at America's NIST say that only a quantum device can produce true randomness, and that everything else produced by classical physics is just not. They say:
No device that relies on classical physical principles or operations can certify that its output is absolutely unpredictable.
News(?) to the UK government who regularly certify ERNIE running the country's national savings scheme. And he runs on diodes. Are NIST suggesting that he can be predicted, perhaps in the future with bigger computers?