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I recently championed quantum key distribution networks. This has led me to also question quantum random number generators. It appears that randomness is randomness, even if made by custom quantum hardware featuring lasers and photon genies.

It would seem that there is a great deal of chaff and hype surrounding quantum generation of anything at all, and so I'm left wondering what is the qualitative difference between:-

quantis

which is a 4 Mbps quantum beam splitter[*] selling for ~€1300 and

die

when coupled with a simple von Neuman[+] extraction technique?

This is not a facile question. I'm interested in any tangible substantive difference between the two sequences of random bits other than speed. Are they just as random if not as fast? And therefore are quantum RNGs further examples of electronic snake oil?

It's easy to immediately berate such quantum hardware as pure marketing. No one's as cynical as I am, but the evidence suggests that there are non gullible people (indeed commentators, universities and IT organisations) buying these. £M's are globally spent on researching new /faster quantum generators. NIST has one. Why should they bother demonstrating measurements outside of the cone of influence when they could use a smart card or dice? Are all of the people being fooled all of the time? That's meant to be impossible.

[*] A laser beam is split with a semi-mirror and detection of photons in the two resulting beams produces random bits. There is a white paper here describing this kit.

[+] This experiment produces independent and identically distributed random bits (not 1 - 6) due to the shaker cup eliminating correlations between throws, and the von Neumann extractor removing die bias. 1 truly random bit is generated every two throws (slightly less on average).

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    $\begingroup$ The beam splitter is snake oil. You get perfectly unpredictable random numbers by any smart card chip, which costs only a few euros. $\endgroup$
    – user27950
    Commented Oct 1, 2017 at 8:42
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    $\begingroup$ I don't know why you would bring a Von Neumann extractor into this, if your dice are biased get better dice $\endgroup$
    – daniel
    Commented Oct 2, 2017 at 8:15
  • $\begingroup$ This suggests that the toss of a symmetrical die is not a perfectly random of cource this is after throw $\endgroup$
    – kelalaka
    Commented Oct 12, 2018 at 20:46
  • $\begingroup$ @kelalaka Shaker cup + von Neumann. $\endgroup$
    – Paul Uszak
    Commented Oct 12, 2018 at 20:53

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From the manufacturer's website:

Quantis uses Quantum Physics to create truly random numbers

Existing randomness sources can be grouped in two classes: software solutions, which can only generate pseudo-random bit streams, and physical (hardware) sources. Software solutions are not capable of providing true randomness as they are based on deterministic computer programs. Instead, they rely on external entropy sources to build up randomness, but these are slow and inefficient, and the quality of the randomness may be difficult to verify. In the latter – hardware RNGs – most random number generators still rely on classical physics to produce what looks like a random stream of bits. However, in reality, determinism is hidden behind complexity for such RNGs without real quantum random properties.

They claim that hardware random number generators which do not use quantum properties are actually deterministic but this determinism is hidden. This is complete nonsense.

There is no evidence that this is true and no theoretical model supporting it.

Even if the universe was completely deterministic as long as the process generating the output is hidden (as they claim) the output will still appear random for all intents and purposes. Randomness is not necessarily a fact about the universe but about the lack of knowledge of an adversary.

Saying that the universe is completely deterministic but that their quantum random number generator works would require the universe to receive no feedback from quantum effects. If this was true we could also not measure them.

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    $\begingroup$ In particular, to claim that other hardware RNGs are completely deterministic, they need to claim that they are not chaotic systems, as a chaotic system would amply initially tiny deltas (from quantum effects) into large output changes after some moderate multiple of the inverse of the Lyapunov exponent... $\endgroup$
    – poncho
    Commented Oct 2, 2017 at 2:35
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    $\begingroup$ They use deterministic post-conditioning with a CSPRNG. Quoting the manufacturer on the only version that has a letter of approval by a CC authority: "The validation of the AIS 31 PTG.3 level was issued by the ANSSI the 19th August 2014. It applies only to dedicated AIS31 versions of Quantis (QUANTIS AIS31) which are provided with the certified post-processing software". This is sound, but I'm more confident no goof creeps with the dice. $\endgroup$
    – fgrieu ♦
    Commented Oct 2, 2017 at 5:48
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    $\begingroup$ I wouldn't go as far as to call it complete nonsense. It is true on its face, but it is a red herring. Whether the determinism is "hidden" or not is irrelevant if it still cannot be predicted by an attacker. From a quantum physics standpoint, it is an open question whether or not quantum probability is truly unpredictable. The general consensus (in the form of mere educated guesses from the leading minds in QM) currently is that it is, and that there is no underlying determinism, just pure probability in these events. $\endgroup$
    – forest
    Commented Mar 25, 2018 at 23:10
  • $\begingroup$ Every analysis that I've seen of hardware silicon random number generators is incorrect btw. The "thermal noise" is actually two-way shot noise in the channel, and if you do the thermal noise derivation you can prove it is deterministic. The only reason that these devices work is because they are modeled incorrectly, which is sort of hilarious. The two-way shot noise gives a provably random result. Also, you can prove that Pauli vectors are truly random (arxiv.org/abs/0811.4542), which is why most people in the quantum random space say that their generators are better. $\endgroup$
    – b degnan
    Commented Oct 12, 2018 at 14:37
  • $\begingroup$ @bdegnan It's a laser beam splitter using a semi-mirror. It absolutely does not rely on thermal noise of any sort. You'll find the two detectors' signals are many dB above the noise floor. This is a well vetted and common optical technique for non deterministic bit generation. Some piccies here but ignore the first kiddie's half. $\endgroup$
    – Paul Uszak
    Commented Oct 12, 2018 at 16:39
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Quantum RNGs are theoretically random, since you can't even imagine a way someone could predict their output.

All other RNGs are less-than-perfectly random.

So "true" RNGs not based on quantum physics are not actually "true."

And what might be considered a "pseudo" RNG for one purpose, could be considered "cryptographically-secure" for another.

Rolling dice is less random than quantum physics, theoretically. But it's practically the same.

Like someone else pointed out, if you remember that randomness is nothing more than the quality of being difficult to predict, all confusion vanishes.

At least, it does for me.

EDIT:

The objections raised in the comments are based on a misunderstanding. A die roll is non-random to the extent one can predict the outcome other than 1/6th of the time. Quantum physics is non-random to the extent one can predict whether an atom decays before it reaches its half-life other than 50% of the time. If you want random numbers in a different range than 1 through 6 from a six-sided die then you are complicating a very simple thought experiment unnecessarily, and likewise if you want a number other than 0 or 1 from the crude "will an atom decay before its half-life" RNG.

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    $\begingroup$ This answer defends that there is a qualitative difference between RNGs based on 1) a quantum source 2) a dice; both followed by Von Neumann debiasing (both need that conditioning step). Yet the only differences stated are A) the first generator is a quantum RNG, when the other is considered not so; but aside from the name, the answer gives no explicit difference. B) It is stated that the dice-based RNG must be "less-than-perfectly random", but no argument is given for that (and I have trouble finding such argument that clearly could not apply to an actual, physical quantum RNG as depicted). $\endgroup$
    – fgrieu ♦
    Commented Oct 12, 2018 at 6:31
  • $\begingroup$ Quantum RNGs are theoretically random, since you can't even imagine a way someone could predict their output. All other RNGs are less-than-perfectly random. So "true" RNGs not based on quantum physics are not actually "true."— Reductio ad absurdum! Sorry to say so, but that's a so called "argument from ignorance". Just because it has "quantum" in the name doesn't mean it's any better. Proof for that does not exist. Also, your claim would mean that Von Neumann debaising is flawed in some way, for which we also do not have any proof. $\endgroup$
    – e-sushi
    Commented Oct 12, 2018 at 15:27
  • $\begingroup$ Both the dice-based generator and the quantum-based generator need some debiasing. Both could be flawed despite Von Neumann debiasing if the inputs before debiaser are correlated. For a dice that could be a mechanical dice thrower that rolls the dice very regularly, from an insufficient height, and starting from the position of the previous throw (some humans reportedly manage to have some influence on dice throw results). For a generator based on some quantum event, that could be if the detector for that event has some memory of the past, which is not unreasonable. $\endgroup$
    – fgrieu ♦
    Commented Oct 12, 2018 at 15:41
  • $\begingroup$ Err, you may be right about the misunderstanding. The experiment produces independent and identically distributed bits due to the shaker cup (+ vigorous wrist action) and the VN debiaser. It doesn't produce 1 - 6. And how are you predicting spontaneous radioactive decay with such certainty? Isn't it a bit randomish? $\endgroup$
    – Paul Uszak
    Commented Oct 12, 2018 at 20:50
  • $\begingroup$ Based on my understanding of the VN debiaser it can't turn a string of correlated bits into perfectly random bits. So your imperfect, although vigorous, wrist action and die can't produce perfectly random numbers even with a VN debiaser (I did not take a debiaser into account in my answer); since the die rolls are not perfectly uncorrelated. Quantum physics says it's 100% certain that one cannot predict with better than 50% success whether any given atom decays before its half-life. Not sure if that answers your question, or why this is being treated as if it's so complicated. $\endgroup$
    – Meler Lawler
    Commented Oct 13, 2018 at 0:46

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