Do you really need a QC in order to have a really unpredictable stream of bits?

0. Preliminaries:

This post has reference to Roger Schlafly’s recent post [^] in which he refers to Prof. Scott Aaronson’s post touching on the issue of the randomness generated by a QC vis-a-vis that obtained using the usual classical hardware [^], in particular, to Aaronson’s remark:

“the whole point of my scheme is to prove to a faraway skeptic—one who doesn’t trust your hardware—that the bits you generated are really random.”

I do think (based on my new approach to QM [(PDF) ^]) that building a scalable QC is an impossible task.

I wonder if they (the QC enthusiasts) haven’t already begun realizing the hopelessness of their endeavours, and thus haven’t slowly begun preparing for a graceful exit, say via the QC-as-a-RNG route.

While Aaronson’s remarks also saliently involve the element of the “faraway” skeptic, I will mostly ignore that consideration here in this post. I mean to say, initially, I will ignore the scenario in which you have to transmit random bits over a network, and still have to assure the skeptic that what he was getting at the receiving end was something coming “straight from the oven”—something which was not tampered with, in any way, during the transit. The skeptic would have to be specially assured in this scenario, because a network is inherently susceptible to a third-party attack wherein the attacker seeks to exploit the infrastructure of the random keys distribution to his advantage, via injection of systematic bits (i.e. bits of his choice) that only appear random to the intended receiver. A system that quantum-mechanically entangles the two devices at the two ends of the distribution channel, does logically seem to have a very definite advantage over a combination of ordinary RNGs and classical hardware for the network. However, I will not address this part here—not for the most part, and not initially, anyway.

Instead, for most of this post, I will focus on just one basic question:

Can any one be justified in thinking that an RNG that operates at the QM-level might have even a slightest possible advantage, at least logically speaking, over another RNG that operates at the CM-level? Note, the QM-level RNG need not always be a general purpose and scalable QC; it can be any simple or special-purpose device that exploits, and at its core operates at, the specifically QM-level.

Even if I am a 100% skeptic of the scalable QC, I also think that the answer on this latter count is: yes, perhaps you could argue that way. But then, I think, your argument would still be pointless.

Let me explain, following my approach, why I say so.


2. RNGs as based on nonlinearities. Nonlinearities in QM vs. those in CM:

2.1. Context: QM involves IAD:

QM does involve either IAD (instantaneous action a distance), or very, very large (decidedly super-relativistic) speeds for propagation of local changes over all distant regions of space.

From the experimental evidence we have, it seems that there have to be very, very high speeds of propagation, for even smallest changes that can take place in the \Psi and V fields. The Schrodinger equation assumes infinitely large speeds for them. Such obviously cannot be the case—it is best to take the infinite speeds as just an abstraction (as a mathematical approximation) to the reality of very, very high actual speeds. However, the experimental evidence also indicates that even if there has to be some or the other upper bound to the speeds v, with v \gg c, the speeds still have to be so high as to seemingly approach infinity, if the Schrodinger formalism is to be employed. And, of course, as you know it, Schrodinger’s formalism is pretty well understood, validated, and appreciated [^]. (For more on the speed limits and IAD in general, see the addendum at the end of this post.)

I don’t know the relativity theory or the relativistic QM. But I guess that since the electric fields of massive QM particles are non-uniform (they are in fact singular), their interactions with \Psi must be such that the system has to suddenly snap out of some one configuration and in the same process snap into one of the many alternative possible configurations. Since there are huge (astronomically large) number of particles in the universe, the alternative configurations would be {astronomically large}^{very large}—after all, the particles positions and motions are continuous. Thus, we couldn’t hope to calculate the propagation speeds for the changes in the local features of a configuration in terms of all those irreversible snap-out and snap-in events taken individually. We must take them in an ensemble sense. Further, the electric charges are massive, identical, and produce singular and continuous fields. Overall, it is the ensemble-level effects of these individual quantum mechanical snap-out and snap-in events whose end-result would be: the speed-of-light limitation of the special relativity (SR). After all, SR holds on the gross scale; it is a theory from classical electrodynamics. The electric and magnetic fields of classical EM can be seen as being produced by the quantum \Psi field (including the spinor function) of large ensembles of particles in the limit that the number of their configurations approaches infinity, and the classical EM waves i.e. light are nothing but the second-order effects in the classical EM fields.

I don’t know. I was just loud-thinking. But it’s certainly possible to have IAD for the changes in \Psi and V, and thus to have instantaneous energy transfers via photons across two distant atoms in a QM-level description, and still end up with a finite limit for the speed of light (c) for large collections of atoms.

OK. Enough of setting up the context.

2.2: The domain of dependence for the nonlinearity in QM vs. that in CM:

If QM is not linear, i.e., if there is a nonlinearity in the \Psi field (as I have proposed), then to evaluate the merits of the QM-level and CM-level RNGs, we have to compare the two nonlinearities: those in the QM vs. those in the CM.

The classical RNGs are always based on the nonlinearities in CM. For example:

  • the nonlinearities in the atmospheric electricity (the “static”) [^], or
  • the fluid-dynamical nonlinearities (as shown in the lottery-draw machines [^], or the lava lamps [^]), or
  • some or the other nonlinear electronic circuits (available for less than $10 in hardware stores)
  • etc.

All of them are based on two factors: (i) a large number of components (in the core system generating the random signal, not necessarily in the part that probes its state), and (ii) nonlinear interactions among all such components.

The number of variables in the QM description is anyway always larger: a single classical atom is seen as composed from tens, even hundreds of quantum mechanical charges. Further, due to the IAD present in the QM theory, the domain of dependence (DoD) [^] in QM remains, at all times, literally the entire universe—all charges are included in it, and the entire \Psi field too.

On the other hand, the DoD in the CM description remains limited to only that finite region which is contained in the relevant past light-cone. Even when a classical system is nonlinear, and thus gets crazy very rapidly with even small increases in the number of degrees of freedom (DOFs), its DoD still remains finite and rather very small at all times. In contrast, the DoD of QM is the whole universe—all physical objects in it.

2.3 Implication for the RNGs:

Based on the above-mentioned argument, which in my limited reading and knowledge Aaronson has never presented (and neither has any one else either, basically because they all continue to believe in von Neumann’s characterization of QM as a linear theory), an RNG operating at the QM level does seem to have, “logically” speaking, an upper hand over an RNG operating at the CM level.

Then why do I still say that arguing for the superiority of a QM-level RNG is still pointless?


3. The MVLSN principle, and its epistemological basis:

If you apply a proper epistemology (and I have in my mind here the one by Ayn Rand), then the supposed “logical” difference between the two descriptions becomes completely superfluous. That’s because the quantities whose differences are being examined, themselves begin to lose any epistemological standing.

The reason for that, in turn, is what I call the MVLSN principle: the law of the Meaninglessness of the Very Large or very Small Numbers (or scales).

What the MVLSN principle says is that if your argument crucially depends on the use of very large (or very small) quantities and relationships between them, i.e., if the fulcrum of your argument rests on some great extrapolations alone, then it begins to lose all cognitive merit. “Very large” and “very small” are contextual terms here, to be used judiciously.

Roughly speaking, if this principle is applied to our current situation, what it says is that when in your thought you cross a certain limit of DOFs and hence a certain limit of complexity (which anyway is sufficiently large as to be much, much beyond the limit of any and every available and even conceivable means of predictability), then any differences in the relative complexities (here, of the QM-level RNGs vs. the CM-level RNGs) ought to be regarded as having no bearing at all on knowledge, and therefore, as having no relevance in any practical issue.

Both QM-level and CM-level RNGs would be far too complex for you to devise any algorithm or a machine that might be able to predict the sequence of the bits coming out of either. Really. The complexity levels already grow so huge, even with just the classical systems, that it’s pointless trying to predict the the bits. Or, to try and compare the complexity of the classical RNGs with the quantum RNGs.

A clarification: I am not saying that there won’t be any systematic errors or patterns in the otherwise random bits that a CM-based RNG produces. Sure enough, due statistical testing and filtering is absolutely necessary. For instance, what the radio-stations or cell-phone towers transmit are, from the viewpoint of a RNG based on radio noise, systematic disturbances that do affect its randomness. See random.org [^] for further details. I am certainly not denying this part.

All that I am saying is that the sheer number of DOF’s involved itself is so huge that the very randomness of the bits produced even by a classical RNG is beyond every reasonable doubt.

BTW, in this context, do see my previous couple of posts dealing with probability, indeterminism, randomness, and the all-important system vs. the law distinction here [^], and here [^].


4. To conclude my main argument here…:

In short, even “purely” classical RNGs can be way, way too complex for any one to be concerned in any way about their predictability. They are unpredictable. You don’t have to go chase the QM level just in order to ensure unpredictability.

Just take one of those WinTV lottery draw machines [^], start the air flow, get your prediction algorithm running on your computer (whether classical or quantum), and try to predict the next ball that would come out once the switch is pressed. Let me be generous. Assume that the switch gets pressed at exactly predictable intervals.

Go ahead, try it.


5. The Height of the Tallest Possible Man (HTPM):

If you still insist on the supposedly “logical” superiority of the QM-level RNGs, make sure to understand the MVLSN principle well.

The issue here is somewhat like asking this question:

What could possibly be the upper limit to the height of man, taken as a species? Not any other species (like the legendary “yeti”), but human beings, specifically. How tall can any man at all get? Where do you draw the line?

People could perhaps go on arguing, with at least some fig-leaf of epistemological legitimacy, over numbers like 12 feet vs. 14 feet as the true limit. (The world record mentioned in the Guinness Book is slightly under 9 feet [^]. The ceiling in a typical room is about 10 feet high.) Why, they could even perhaps go like: “Ummmm… may be 12 feet is more likely a limit than 24 feet? whaddaya say?”

Being very generous of spirit, I might still describe this as a borderline case of madness. The reason is, in the act of undertaking even just a probabilistic comparison like that, the speaker has already agreed to assign non-zero probabilities to all the numbers belonging to that range. Realize, no one would invoke the ideas of likelihood or probability theory if he thought that the probability for an event, however calculated, was always going to be zero. He would exclude certain kinds of ranges from his analysis to begin with—even for a stochastic analysis. … So, madness it is, even if, in my most generous mood, I might regard it as a borderline madness.

But if you assume that a living being has all the other characteristic of only a human being (including being naturally born to human parents), and if you still say that in between the two statements: (A) a man could perhaps grow to be 100 feet tall, and (B) a man could perhaps grow to be 200 feet tall, it is the statement (A) which is relatively and logically more reasonable, then what the principle (MVLSN) says is this: “you basically have lost all your epistemological bearing.”

That’s nothing but complex (actually, philosophic) for saying that you have gone mad, full-stop.

The law of the meaningless of the very large or very small numbers does have a certain basis in epistemology. It goes something like this:

Abstractions are abstractions from the actually perceived concretes. Hence, even while making just conceptual projections, the range over which a given abstraction (or concept) can remain relevant is determined by the actual ranges in the direct experience from which they were derived (and the nature, scope and purpose of that particular abstraction, the method of reaching it, and its use in applications including projections). Abstractions cannot be used in disregard of the ranges of the measurements over which they were formed.

I think that after having seen the sort of crazy things that even simplest nonlinear systems with fewest variables and parameters can do (for instance, which weather agency in the world can make predictions (to the accuracy demanded by newspapers) beyond 5 days? who can predict which way is the first vortex going to be shed even in a single cylinder experiment?), it’s very easy to conclude that the CM-level vs. QM-level RNG distinction is comparable to the argument about the greater reasonableness of a 100 feet tall man vs. that of a 200 feet tall man. It’s meaningless. And, madness.


6. Aaronson’s further points:

To be fair, much of the above write-up was not meant for Aaronson; he does readily grant the CM-level RNGs validity. What he says, immediately after the quote mentioned at the beginning of this post, is that if you don’t have the requirement of distributing bits over a network,

…then generating random bits is obviously trivial with existing technology.

However, since Aaronson believes that QM is a linear theory, he does not even consider making a comparison of the nonlinearities involved in QM and CM.

I thought that it was important to point out that even the standard (i.e., Schrodinger’s equation-based) QM is nonlinear, and further, that even if this fact leads to some glaring differences between the two technologies (based on the IAD considerations), such differences still do not lead to any advantages whatsoever for the QM-level RNG, as far as the task of generating random bits is concerned.

As to the task of transmitting them over a network is concerned, Aaronson then notes:

If you do have the requirement, on the other hand, then you’ll have to do something interesting—and as far as I know, as long as it’s rooted in physics, it will either involve Bell inequality violation or quantum computation.

Sure, it will have to involve QM. But then, why does it have to be only a QC? Why not have just special-purpose devices that are quantum mechanically entangled over wires / EM-waves?

And finally, let me come to yet another issue: But why would you at all have to have that requirement?—of having to transmit the keys over a network, and not using any other means?

Why does something as messy as a network have to get involved for a task that is as critical and delicate as distribution of some super-specially important keys? If 99.9999% of your keys-distribution requirements can be met using “trivial” (read: classical) technologies, and if you can also generate random keys using equipment that costs less than $100 at most, then why do you have to spend billions of dollars in just distributing them to distant locations of your own offices / installations—especially if the need for changing the keys is going to be only on an infrequent basis? … And if bribing or murdering a guy who physically carries a sealed box containing a thumb-drive having secret keys is possible, then what makes the guys manning the entangled stations suddenly go all morally upright and also immortal?

From what I have read, Aaronson does consider such questions even if he seems to do so rather infrequently. The QC enthusiasts, OTOH, never do.

As I said, this QC as an RNG thing does show some marks of trying to figure out a respectable exit-way out of the scalable QC euphoria—now that they have already managed to wrest millions and billions in their research funding.

My two cents.


Addendum on speed limits and IAD:

Speed limits are needed out of the principle that infinity is a mathematical concept and cannot metaphysically exist. However, the nature of the ontology involved in QM compels us to rethink many issues right from the beginning. In particular, we need to carefully distinguish between all the following situations:

  1. The transportation of a massive classical object (a distinguishable, i.e. finite-sized, bounded piece of physical matter) from one place to another, in literally no time.
  2. The transmission of the momentum or changes in it (like forces or changes in them) being carried by one object, to a distant object not in direct physical contact, in literally no time.
  3. Two mutually compensating changes in the local values of some physical property (like momentum or energy) suffered at two distant points by the same object, a circumstance which may be viewed from some higher-level or abstract perspective as transmission of the property in question over space but in no time. In reality, it’s just one process of change affecting only one object, but it occurs in a special way: in mutually compensating manner at two different places at the same time.

Only the first really qualifies to be called spooky. The second is curious but not necessarily spooky—not if you begin to regard two planets as just two regions of the same background object, or alternatively, as two clearly different objects which are being pulled in various ways at the same time and in mutually compensating ways via some invisible strings or fields that shorten or extend appropriately. The third one is not spooky at all—the object that effects the necessary compensations is not even a third object (like a field). Both the interacting “objects” and the “intervening medium” are nothing but different parts of one and the same object.

What happens in QM is the third possibility. I have been describing such changes as occurring with an IAD (instantaneous action at a distance), but now I am not too sure if such a usage is really correct or not. I now think that it is not. The term IAD should be reserved only for the second category—it’s an action that gets transported there. As to the first category, a new term should be coined: ITD (instantaneous transportation to distance). As to the third category, the new term could be IMCAD (instantaneous and mutually compensating actions at a distance). However, this all is an afterthought. So, in this post, I only have ended up using the term IAD even for the third category.

Some day I will think more deeply about it and straighten out the terminology, may be invent some or new terms to describe all the three situations with adequate directness, and then choose the best… Until then, please excuse me and interpret what I am saying in reference to context. Also, feel free to suggest good alternative terms. Also, let me know if there are any further distinctions to be made, i.e., if the above classification into three categories is not adequate or refined enough. Thanks in advance.


A song I like:

[A wonderful “koLi-geet,” i.e., a fisherman’s song. Written by a poet who hailed not from the coastal “konkaN” region but from the interior “desh.” But it sounds so authentically coastal… Listening to it today instantly transported me back to my high-school days.]

(Marathi) “suTalaa vaadaLi vaaraa…”
Singing, Music and Lyrics: Shaahir Amar Sheikh

 


History: Originally published on 2019.07.04 22:53 IST. Extended and streamlined considerably on 2019.07.05 11:04 IST. The songs section added: 2019.07.05 17:13 IST. Further streamlined, and also further added a new section (no. 6.) on 2019.07.5 22:37 IST. … Am giving up on this post now. It grew from about 650 words (in a draft for a comment at Schlafly’s blog) to 3080 words as of now. Time to move on.

Still made further additions and streamlining for a total of ~3500 words, on 2019.07.06 16:24 IST.

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