Quanta delenda est!

In a sensible world, where science journalists understood the science they are trying to communicate, and science editors didn’t regard their readers as dimwits with the attention span of a smoked salmon, I wouldn’t be writing this post. Unfortunately, we don’t live in that world.

And where do we live? We live in a planet where a famous popular science magazine has written an article claiming that these two pre-prints [1, 2] “overturn” my results on the experimental disproof of real quantum physics.

For the record: I disagree, so do my co-authors and so does any expert in quantum nonlocality, the topic of my work.

Does Quanta magazine care? No. In fact, as we will see, they censored the opinion of the only expert interviewed because it clashed with the narrative of this travesty of a science communication paper.

This leaves me no other choice but to do Quanta’s job. In the next pages, I am going to explain what my paper is about, what the two pre-prints are about, and why there’s no connection between our work and theirs. And I will do it in such a way that anyone, anyone! -pirate, ship wrecker, pure finder or Quanta editor- can understand it.

Preliminaries

One of the reasons why so many people got confused is that the three papers involved use different meanings of the word “theory”. To sort out this mess, throughout this post I will stick to a very strict terminology.

Consequently, I will use the word “theory” to only mean a series of rules that allow making concrete physical predictions.

For example, consider a solar system with 8 planets, with known initial speeds and positions. This, together with Newton’s laws, constitutes a theory: we can use it to predict the future (or past) positions and speeds of each planet.

In this sense, all theories are falsifiable: all it takes is observing a violation of their very concrete predictions. In this example, the theory might predict that Mars will collide with Jupiter next year. If that doesn’t happen, then the theory is falsified.

Connected with the concept of theory is the notion of “representation”. A representation of a theory is the mathematical language we use to describe it, or the way we choose to express our predictions. For the 8-planet theory, one can use the Cartesian coordinates  to represent the position of each planet with respect to the Sun. Alternatively, one could specify the distance \(r\) to the sun, together with the two Euler angles \(\theta, \varphi\), see the picture:

Both representations are equivalent ways of referring to the position of a planet. Indeed, one can switch from one representation to the other using some mathematical formulas.

The 8-planet theory has infinitely many representations. For instance, one could define vectors representing the sum and difference between the position and momentum of each planet; or something more complicated. However, no matter the representation, the predictions are always the same.

Now, the last definition: the concept of “foil”. A foil refers to the structures that theories within a set have in common. For example, suppose that we wished to define the foil encompassing all physical theories that we regard as “classical”. And think: what do the 8-planet theory, the theory of perfect gases and electromagnetism have in common?

The answer: at any time \(t\), the state of the considered physical system can be described by a list of fundamental properties (positions and speeds, in the first case; temperature, pressure and volume in the second; the strength and direction of electric and magnetic fields in the third). The result of any observation at time \(t\) is a function of these fundamental properties. Each of these properties is, moreover, localized in some region of space, so that observations at any place only depend on the local properties around (and not, say, on properties localized many light-years away).

This is the foil that we call “classical physics”. It is very abstract, and necessarily so, to faithfully describe our everyday experience of the world.

Let us now turn to quantum physics. In the standard representation of the quantum foil, the state of a physical system is described by a vector or list of complex numbers called the wave-function [from now on, I assume that the reader is familiar with complex numbers, e.g.: \(-1+\frac{3i}{2}\). If the reader ignores the meaning of "i" in the expression above, then I recommend them to read this now and then come back to the post]. The name "wave-function" is misleading, because the wave-function is not a wave. It is, however, a function, in the sense that any vector is a function assigning a value to each vector index.

Observations or measurements in the quantum foil are represented by tables of complex numbers called “operators”. In the quantum foil, the outcome of most experiments is not determined by the prior state of the system; rather, what the wave-function determines are the probabilities of obtaining one outcome or another. For instance, if the initial wave-function of the photon (the particle that makes up light) below is  \( \bigg(i\sqrt{\frac{2}{3}},\sqrt{\frac{1}{3}}\bigg) \), then the probability that it makes detector 1 click is \(\frac{1}{3}\).

Here is a rough comparison between how classical and quantum foils model physical systems:

Foil	States	Observation	Prediction
Classical	List of properties	Function of state properties	Deterministic
Quantum	Wave-function	Operator	Probabilistic

As we mentioned already, physical theories can be easily falsified, that is, if they happen to be incorrect. But how about foils?

Well, that is much more complicated. You see, foils do not make predictions; theories do. To return to the example of the planets: suppose that, after all, Mars doesn’t collide with Jupiter. Does that mean that classical physics is over? Not at all. Probably one could come up a 20-planet theory that fits all the data. The theory would, however, demand the existence of 12 non-observed planets. What happens if we do not see them, is that the end of classical physics? Hell, no. Because a theory with 200 extra hidden asteroids might also fit the data and explain why we didn’t see anything in the 12 spots we just looked. Alternatively, one could stick to 8 planets and no asteroids and tinker with Newton’s laws instead, making, e.g., the gravitational force be proportional to the inverse of the distance instead of the inverse of the distance squared. Or one could argue that the spots we observe with telescopes are, in fact, not planets, but the result of a bizarre world conspiracy of fireflies. And so on, ad infinitum.

To falsify a foil, one needs to conduct an experiment whose outcomes are incompatible with any theory fitting the foil. In other words, we are speaking of a single experiment capable of disproving infinitely many theories at once.

Impossible? No. In fact, we physicists have already falsified a foil, the classical foil. This happened in 2015 in three quantum experiments, conducted in Delft (the Netherlands), Vienna (Austria) and Boulder (USA).

The idea, very old, was first conceived by Irish physicist John S. Bell. He realized that, in experiments involving two separate labs, the classical foil predicted some statistical constraints that can be violated by quantum theories.

More specifically: experimentalists Alice and Bob, who control different labs, are distributed a pair of physical systems by a source, see the figure: 

 What kind of systems? Two electrons, two semiconductors, a beetroot and a pineapple, that doesn’t matter. Alice’s experiment allows her to estimate two properties of her system. We could call these two properties “Tom” and “Jerry”, but tradition demands the more sober names “0” and “1”. The same with Bob: he can also measure two properties “0” and “1” of his system. The outcome of each experiment at each lab can be either “-1” or “1”.

Now, my dear reader, here come the maths.

“Wait! The maths!? But… isn’t this science communication?”

No! This is theoretical physics communication, and maths are unavoidable. So get a grip and keep reading. 

Call \(A_x\) the result (remember: -1 or 1) that Alice obtains when she measures property \(x\) (remember: 0 or 1); call \(B_x\) (-1 or 1) the result that Bob obtains when he measures property \(y\) (0 or 1). If we repeat the experiment several times, namely, if the source sends Alice and Bob many pairs of systems, one after the other, and each time Alice and Bob choose randomly which properties  and  to measure, then Alice and Bob can estimate the product average:$$\langle A_xB_y\rangle=\frac{\mbox{sum of products of Alice's and Bob's outcomes when they chose the same }x,y}{\frac{\mbox{# of distributed pairs}}{4}}.$$ This number can take values between -1 and 1. Now, consider the quantity:\[ CHSH = \left\langle A_0B_0\right\rangle + \left\langle A_1B_0\right\rangle + \left\langle A_0B_1\right\rangle - \left\langle A_1B_1\right\rangle \]This value, which can only be estimated by conducting lots of experiments, is known as the Clauser-Horn-Shimony-Holt (CHSH) parameter. Clauser et al. showed that, if a classical theory describes Alice and Bob’s experiment then the CHSH parameter cannot exceed 2. Therefore, if one could conduct an experiment that produced a CHSH value greater than 2, one would have refuted the whole classical foil.

As it turns out, standard quantum theory predicts that, in experiments where the distributed systems are photons and the two measured properties are light polarization along two different directions, then one can achieve values of the CHSH parameter close to 2.82. This very clever observation inaugurated the field of quantum nonlocality, a.k.a. Bell nonlocality, and won Clauser the 2022 Physics Nobel Prize.

The famous “loophole-free Bell experiments” conducted in 2015 returned CHSH values (or some variant thereof) beyond 2. These experimental results do not prove that we live in a quantum world (for all we know, it is impossible to prove a foil); however, they disprove all classical theories. For the first time in history, a whole foil had been falsified!

[Yes, I just used an exclamation mark. Contrary to popular culture characterizations, actual scientists are neither emotionless robots nor crazy maniacs, did you know? What, you didn’t!? You pleb! You'll be sent to one of the 200 hidden asteroids as soon as my galactic army conquers the Earth!]

Now, let us come to the matter at hand.

Real quantum physics

So far, we have only mentioned two foils: the classical and the quantum. Are there more? This is a very fundamental question. Suppose that the answer were “no”. Since Bell experiments proved that classical physics is not universal, it would follow that our world must be described by some theory belonging to the quantum foil.

Unfortunately, the answer to that question is “yes”: at least over the paper, one can construct examples of physical theories that fit neither the classical nor the quantum foil. Most non-quantum, non-classical foils are just toy models, that is, we physicists do not seriously believe that they describe our world. There is, however, one foil that is as plausible as the quantum foil is, and as plausible as the classical foil was. In this post, I will call it “real quantum physics”.

Real quantum physics is the result of taking the standard representation of the quantum foil, where states are described by lists of complex numbers; and observables, as matrices of complex numbers, and demanding all numbers therein to have no imaginary part.

The resulting foil is fascinating.

First, real quantum physics allows carrying out quantum computing, quantum teleportation and quantum cryptography. In this sense, real quantum physics is much closer to quantum than to classical physics.

Second, real quantum physics is much weirder than both classical and quantum physics. To explain why, we need to introduce the notion of composite systems.

A composite system is a physical system made of two or more subsystems. E.g.: an atom is a composite system made of protons, neutrons and electrons. And you are a composite of (hopefully!) two arms, two legs, a torso and a head. In both quantum and classical theories, the overall state of a composite system can be determined by probing each subsystem independently. For example, in classical physics, to verify that you have a red apple and I have a yellow pear, it is enough that you look at your apple and I look at my pear. Namely, it is not required that we bring the apple and the pear together and make them interact. The same holds in quantum physics: to find the polarization state of two photons, it is enough to measure each photon individually and compare the results.

In real quantum physics, though, composite systems can have holistic properties that can only be accessed when we put all subsystems together. This strange feature of real quantum physics is called non-local tomography. For instance, pairs of real quantum photons have a physical property that can take values 0, 1. This property cannot be estimated by measuring each photon and comparing the results, so the two people holding the photons would have to come together to learn this “secret bit”, which could in principle encode which of them will inherit the family fortune.

Now, given two foil representations, it is in general very difficult to tell if they describe the same foil, namely, if there exists a one-to-one correspondence between states and observations in one representation and the other. However, because of non-local tomography, we know that the real quantum foil is neither the quantum nor the classical foil: it is a different type of physics altogether.

Till recently, real quantum physics was therefore the only known plausible foil still standing against quantum physics. This made many physicists wonder if it would be possible to falsify the real quantum foil through a quantum experiment, in the same way that we falsified the classical foil.

This question was first formulated in 2007. It was quickly followed, in 2009, by a strong no-go result: through Bell experiments, even those involving more than two parties, it is impossible to falsify the real quantum foil. The reason is that the range of values of any statistical quantity one can define in a Bell test, like the CHSH parameter above, is the same in the quantum and in the real quantum foils. Thus, the strategy followed by Bell to falsify classical physics -the only strategy known to falsify whole foils- didn’t apply.

That left the quantum nonlocality community in a weird position. For, suppose that the real quantum foil were, indeed, unfalsifiable with quantum experiments. That would imply that a die-hard fan of real quantum physics living in a quantum world could always find a real quantum theory to accommodate the results of every actual experiment. Such real quantum theories would predict the existence of holistic physical properties that one would never detect, because in fact they wouldn’t exist. That would be fine for the real-quantum fan, who, in order to win the discussion, doesn’t need to predict, just explain experimental data.

Our paper

Things changed in 2021, when my colleagues and I found a way to falsify real quantum physics within quantum physics. Our idea required conducting an experiment over three separate labs, handled by experimenters Alice, Bob and Charlie. Like in a Bell experiment, each lab would be distributed a physical system, which they would probe locally. Unlike in a general three-partite Bell experiment, though, the distribution of the systems would be done by two independent sources, see the figure.

In this scenario, we found a statistical quantity \(B\) that, in the quantum foil, can take values from -8.49 to 8.49. In real quantum theories, though, this quantity can just take values between -7.66 and 7.66. Any experiment reporting a value of \(B\) greater than the last figure would effectively disprove the real quantum foil.

The quantum experiment that we proposed was much more complicated than the loophole-free Bell experiments of 2014 that disproved classical physics. However, in the meantime quantum technology had advanced a lot, so we were confident that an implementation was feasible.

We were right. 

Two experiments quickly followed: one with superconducting circuits; and another one, which we helped to devise, with photon polarization. The two experiments reported values of \(B\) beyond 7.66. There were some loopholes, though, mainly related to the fact that the three labs involved were too close to each other to discard cross-talk effects. Some of these loopholes were closed in this other experiment, where the three labs were separated by hundreds of meters. Although this last experiment still has a loophole, it gives further evidence that the real quantum foil is not rich enough to describe our world.

The other papers

In early 2025, two pre-prints [1, 2]  appeared in arxiv (some repository that physicists use to publicize their results before they get published in a journal). The two papers construct real-valued representations of the quantum foil. This, in itself, is trivial. Take any representation of any foil that involves complex numbers. Replace each complex number by its real and imaginary parts, and, abracadabra!, you have a real-valued representation of the same foil.

Now, we said earlier that real quantum physics is defined by taking the standard representation of the quantum foil and imposing that every number therein be real instead of complex. The merit of the two pre-prints was finding real-valued representations of quantum theory that are very similar to the standard representation of real quantum physics. More specifically, if one replaces just one of the rules of the standard representation of real quantum physics, related to the composition of physical systems, by something with the same flavor, then one obtains a new representation of quantum theory, despite the fact that all numbers involved are real.

We are now ready to spell out the relation between these two pre-prints and our work. There is none. The two pre-prints deal with real-valued representations of the quantum foil; ours, with the real quantum foil. Similar names, completely different concepts. 

So... 

Why the controversy?

Partly, because of the way the two pre-prints originally framed their results. In their narrative, our initial goal was formulating a real-valued representation of quantum physics. However, because we are stupid, we only considered a very restricted class of representations, which we proved could not account for certain quantum experiments. Hence, we wrongly concluded that real-valued representations of the quantum foil didn’t exist.

Enter the authors of the pre-prints, who, like a modern Copernicus, proposed a “more physical, less mathematical” axiom for system composition that did the trick, thence proving that complex numbers were not needed to represent the quantum foil. Thank you, oh Knights of Quantum, you freed the world of the curse of i! You saviors of theoretical physics, there is not enough gold in the planet to forge the \(10^{42}\) power rings that you deserve!

Too bad that this interpretation of our work doesn’t make sense. As explained in our paper, real quantum physics, the subject of our work, was formulated in 1990 by none of us. And with regards to our stance on real-valued representations of quantum physics, the very first sentence of our paper is already very eloquent:

“Without qualification, the question of whether complex numbers are necessary for natural sciences, and, more concretely, for physics, must be answered in the negative”.

Besides, suppose, for the sake of the argument, that our real goal had really been finding a real-valued representation of the quantum foil, and that we had wrongly concluded that we had a mathematical disproof. Then, why would we, in the name of God, have proposed to conduct an experiment? To prove that \(1\not=2\)?

Fortunately for us, such a gross misunderstanding of our results was only shared by a very small minority of researchers from adjacent fields, like quantum computing. The experts in our field, quantum non-locality, had been hearing for years about the problem of falsifying real quantum physics. In general, they appreciated our results and understood that the authors of [1, 2] were simply missing the point.

So, we had nothing to worry about. Right?

And then came Quanta.

And what did Quanta do? Based on the final piece, multiple email exchanges with the author and conversations with some of the people involved, this is my best guess:

First, the journalist accepted the narrative of the two pre-prints acritically. He interviewed the authors of both pre-prints, who unsurprisingly agreed with their own opinions.

Now journalistic integrity demanded that the journalist also asked the authors of the criticized paper for comments. The logical thing would have been to contact me, the corresponding author. Instead, he talked to my co-author Nicolas Gisin.

“What a great opportunity, nonetheless!”, you would think. Surely Nicolas would have explained him exactly what our work was about and the journalist would have realized that he didn’t have a story.

No, my dear reader, no. If my past experience with this magazine is representative, Quanta’s interviews are not to inform the journalist: on the contrary, by the time they take place, the journalist has already decided what story to tell. The real goal of the interviews is collecting non-contextual statements from experts to validate it. Look at them, in this very article. The longest quote has two sentences!

So, Nicolas explained the journalist that his interpretation of our results was ridiculous. So, Jacopo Surace, a quantum information theorist also contacted by the magazine, told him that our results were not “overturned”. And none of that mattered: since none of them could be misquoted to support the narrative of the article, Quanta didn’t include their statements, period.

What about the other interviewees? Although no experts in quantum nonlocality, Vedral and Wootters have worked in the foundations of physics in the past (it can be argued that Wootters invented real quantum physics). Why didn’t they express disagreement with the main premise of the Quanta article?

Perhaps they did. In effect, it wouldn’t surprise me if their comments had been chopped and shuffled to better fit the story. Look at the statements of Wootters’ that made to the final version; they are as non-contextual as any aphorism by Paulo Coelho:

“Quantum theory really is the first physical theory where the complex numbers seem to be right smack in the middle of the theory.“

“For a lot of things, you actually can get away with the real theory.”

“Even when you translate quantum theory into real numbers, you still see the hallmark of complex-number arithmetic.“

Does Wootters agree with the claim that the two pre-prints have overturned our results? I doubt it, but, from the Quanta article, one can’t tell. Ditto with Vedral.

The text was already finished, and Quanta was ready to publish. But then someone in the journal felt the need of including photos of two of my co-authors: Nicolas and Marc-Olivier “Marco” Renou (the rest of us are not even mentioned in the article). So, Nicolas and Marco were contacted one last time.

Savvy Marco, fearing that Quanta might misrepresent our work, wrote back:

Note that our work does not imply that "it is not possible to obtain a mathematical formalism / a theory [he means “representation”] of physics based only on real number that explains quantum physics phenomenon": there are many ways to do this, we prove something like "if one take the 'standard axioms' of quantum theory [foil] (in particular the mathematical way we represent independent systems with a tensor product) and change the complex into real numbers, it does not work".

I know that sentences like "quantum theory is not real" are quite appealing, but they don't represent well what we did :).

Marco concluded his email offering to proof-read the article for mistakes.

And Quanta replied:

“We cannot share drafts in order to maintain our journalistic independence.“

Bravo, Quanta, bravo! You did it again.

My resolution

I got into physics partly thanks to the popular science works by Russian physicist Yakov Perelman (nothing to do with Grigori Perelman, the mathematician who in 2005 refused to accept the Fields medal). In his books, which in my childhood were labeled “recreational physics”, Perelman did his best to explain to the layperson the basics of mechanics, geometry and astronomy.

And he did so in a very imaginative way. I recall with special fondness his revised version of a chapter of Jules Verne’s “From the Earth to the Moon”. Verne had predicted that the main characters, who were traveling inside a giant bullet, would experience weightlessness at the point where the Earth and Moon’s gravitational forces canceled. Perelman pointed out, however, that, since they were in free fall, they should have felt weightless through the whole journey. Consequently, Perelman rewrote one of the chapters of the novel to describe a very chaotic English breakfast, with bacon and eggs floating all around.

I also recall the experiments: surface tension with a needle and a piece of paper, a perfect ball of oil suspended between water and alcohol.

God. What a cool way to learn physics!

Now, go back to the quanta magazine article that started this post. Whom is it directed to? Can you picture a high-school student reading this article and thinking: “this! This is what I want to do with my life!”?

To make matters worse, there is nothing particular about the article, apart from the fact that it personally pissed me off. Take the article about MIP*, for instance. Whom is it going to inspire, people who like the feeling of not understanding a thing? Contrarily, the infamous Quanta article “Physicists Create a Holographic Wormhole Using a Quantum Computer” surely inspired many. That is, until they realized it was a scam; then they probably became flat-earthers, anti-vaxxers or holocaust deniers.

I would understand this shameless disregard for science communication in favor of flashy, click-bait headlines if it came from a popular science journal desperately trying to attract readers to keep itself afloat (I’m looking at you, New Scientist!). But Quanta is a non-profit organization, funded by the Simons foundation with the purpose of “enhancing public understanding of science”. So, why? Why are they doing such a terrible job?

Frankly, I don’t care, not anymore. I say: enough is enough! I say: Quanta delenda est! If every time that Quanta reports the latest advance in quantum information theory it ends up confusing both the masses and the experts, then we quantum information theorists need to take a stance. Therefore, from now on, every time Quanta writes about either quantum information or quantum foundations, I will publish my own take here. And I will make sure that everyone who wishes to understand understands.

It might happen, my dear reader, that, after going through this or some future account of mine, you find that the topic doesn’t interest you at all. That’s NORMAL. Even I, a quantum information theorist, am not thrilled by every single paper in the field. Moreover, some results only look interesting when the reader possesses a large background knowledge: communicating them to the layperson is as difficult as translating a political joke. In my opinion, this applies to the three papers discussed here.

Since I won’t choose the topic, I can’t promise that the journey will be all laughs. Nonetheless, I do promise to commit to the two golden rules of scientific communication:

1) Don’t try to communicate what you don’t understand.

2) Regard readers of popular science as reasonably clever people who wish and deserve to learn.