This is a philosophical point so bear with me a second.
I'm someone who things it very strange when people talk about wave-form collapse, and even stranger when some physicists talk about many worlds (in the universes are duplicated to realize all possible outcomes sense). As if the way to deal with our limited ability to measure the universe around us is by assuming it to be random, and then even more perversely to correct this "God does not play dice" problem by presuming that all outcomes occur in the correct probabilities.
To me it makes much more sense to say. The Universe IS. There is no such thing as "wave-form collapse" or even "wave function evolution." There is no such thing as "time." A excitation exists in some 4 dimensional space. It has a particular shape and you can take cross-sections of it along various planes and compute quantities such as Energy or Charge that happen to be conserved across that class of cross-sections. There are even descriptions of the dynamics of excitation as you continuously vary the cross-section taken. We happen to call one of these local descriptions the Copenhagen interpretation of QM, it is probabilistic and non-deterministic. There is non-local description of the same dynamics, Bohmian QM, it is deterministic.
We use the Copenhagen interpretation because we are interested in the predictive capability of the theory, which Bohmian QM just can't do. If Bohmian QM predicts spin up and its spin down the scientist says "there was a non-local reaction with something outside the experimental apparatus that affected the hidden variable which I can never measure directly." You can start playing games with things and saying I have 99% confidence the hidden variable value is up, and a 99.999% confidence that no non-local interaction will affect that, but its no advantage over Copenhagen, and just saying the outcome is UP 98.999% of the time.
But being predictive IS NOT the same as being descriptive. Don't tell me something *IS* (in the descriptive sense) random just because you can't predict the next number. That's not randomness that just limited intelligence, mathematical ability, and computational capability. Pick an arbitrary sequence from OEIS.org or some sample from the digits of PI and ask people if it is random. NOBODY will say: Oh that's PI beginning at digit 288342341234, but that doesn't make it random. That makes us dumb.
So to the particulars of your comments:
> a signal with maximum entropy, where each bit of the signal carries one bit of information.
"1" was that random or not? Can't say... I need to talk about a sequence of digits.
"3.14159"? -- not random that is "PI."
I don't know what PI is can you explain it to me in less than 6 digits. If you cannot then you cannot compress the stream. If I gave you a thousand digits you could encode a C program that computes PI, but I don't know what C is so now you have to express that. What prevents me from playing the "what is a?" game all day long and forcing you to give me a complete description of every particle in a universe containing a computer that calculates "PI."
Finally we get to the indeterminate sequence of digits generated by your overvolted transistor. You claim that is random because the numbers generated by it cannot be compressed because the underlying process is quantum mechanical and thereby random.
I disagree. If you get to reference something outside the sequence like "PI" then so should I. I will thereby reference the output of your transistor in my deterministic non-local Bohmian description of the dynamics of our static universe. DONE. Its compressed. (self-referential, but compressed)
In other words I reject your statement that "quantum events are not correlated in time with previous events, only with states." I believe they are correlated because the universe has deterministic non-local dynamics, and hidden variables (if we could ever know them) would allow us to correlate the QM events over time.
Another way to put this is to say that you need multiple *INDEPENDENT* outputs from the process in order to calculate its entropy. I REJECT your ability to do so. There is no amount of time-space separation within this universe that you can put between multiple RNGs that will ever make them independent. You need multiple universes to get a correct calculation of entropy. You can only approximate entropy within a single universe.
That said when we calculate this approximate entropy, QM processes seem to have maximal entropy. That does not prove them to be random (descriptive) rather we predict them to be random. If the LHC starts pumping out particles that are all spin up, we would call that new physics and would have to adjust to a world where QM processes are no longer random.
Also the next digit in my sequence was 8, so it wasn't PI anyways.