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Quantum contextuality is just another fancy word for Bohr's complementarity

People keep on rediscovering the old quantum wheel, while they produce and eat lots of šit, too

The popular science media were full of reports that a "magic word" has been found that will enable quantum computers, and the "magic word" is "contextuality". Quantum contextuality is a fancy word for the fact that quantum mechanics doesn't allow you to assume that the quantities you measure objectively had (in the classical sense) the sharp values you ultimately measured before the measurement.

Because of the quantum contextuality, what the measurements reveal depends on the character of the measurements, and not just some would-be objective reality that exists independently of the measurements.

All this journalistic excitement is based on a paper in Nature:

Contextuality supplies the magic for quantum computation by Howard, Wallman, Veitch, Emerson (arXiv, Nature)

Quantum computing: Powered by magic by Bartlett (Nature, semipopular)

... EurekAlert press release, Google News ...
The actual technical paper has a higher percentage of correct statements relatively to the wrong statements than the typical papers published about "the foundations of quantum mechanics" these days. But it is still a bizarre mixture of popular-book-level hype and distortions with some potentially technical stuff in quantum computation.




I won't comment on the truly technical portion of the paper too much. It is building on a credible and important work by Kitaev and Bravyi that is usually known as the "magic state distillation". They showed that it's easier to bring a quantum state to a pure state if this asymptotic pure state lies in certain (magic) directions. Kitaev in particular is a genuine leader of the field of quantum computation and the fault tolerance of quantum computers – which his "magic" paper with Bravyi is addressing – is really the defining reason why he is a leader.




But the new paper about contextuality – and the press that accompanies it – seems to be mostly popular-level philosophy featuring most of the fashionable misconceptions about quantum mechanics.

The press release – and some of the other articles in the media – claim that "contextuality was recognized as a feature of quantum theory almost 50 years ago". Such widespread propositions keep on making me immensely angry.

The word "contextuality" is just a word, one that doesn't mean any new insight whatsoever. The word was introduced to the popular-level physics discourse by John Bell in the 1960s while he was trying to undo the quantum revolution. He would talk about the classical observables he wanted to return to physics – under the name "beables" – and the quantum-like new ones that he wanted to eliminate or to "classicize" – the "contextual" observables. The actual beef of "contextuality" was of course known to the founders of quantum mechanics as early as in the mid 1920s and using different words, Bohr articulated all these things rather clearly – as a lesson to his colleagues who were still finding quantum mechanics difficult – by the mid 1930s. (Yes, Bohr's chosen title was identical to the title of the EPR paper.)

Also, Simon Kochen and Ernst Specker helped the word "contextuality" to spread by their 1967 paper and by their being ambiguous about the fact that they were just confirming Bohr's claims. These guys have always understood quantum mechanics well enough and they were not a part of the Bell-Bohm carcinogenic anti-quantum movement. But the interpretation of their no-go theorem still allowed the very delusions that the theorems eliminated to be legitimized.

People who didn't want to understand that quantum mechanics was right and here to stay – like Albert Einstein – wouldn't be taken seriously in the late 1920s or 1930s or 1940s or, perhaps, 1950s. What changed in the 1960s was only the sociology. Men who were much lousier physicists than Albert Einstein – e.g. David Bohm and John Bell – suddenly gained influence by constant repetition of their anti-scientific delusions and by reorganizing their wrong claims as a political movement of the same kind that began to spread in the 1960s. A whole movement designed to permanently question and undermine the quantum revolution was born and the world hasn't been able to get rid of this nasty tumor by 2014. In fact, it has demonstrably gotten stronger.

The press release mentions the following – cute – example of contextuality:
Imagine turning over a playing card. It will be either a red suit or a black suit - a two-outcome measurement. Now imagine nine playing cards laid out in a grid with three rows and three columns. Quantum mechanics predicts something that seems contradictory – there must be an even number of red cards in every row and an odd number of red cards in every column. Try to draw a grid that obeys these rules and you will find it impossible. It's because quantum measurements cannot be interpreted as merely revealing a pre-existing property in the same way that flipping a card reveals a red or black suit.
This thought experiment has been discussed by Johannes Koelman on this blog in 2012 in quite some detail. He called the gedanken experiment "Albert's chest of quantum drawers" (with socks) and showed that the right predictions can actually be modeled by classical logic as long as we compute some averaged probabilities from "classical mixed states" that, importantly, allow probabilities to be negative.

In the quantitative debates about the foundations of quantum mechanics, the setup is known as the Mermin-Peres magic square and the \(3\times 3\) observables in the square may be written as operators acting on just two qubits (two electrons' spins, for example: be ready for tensor products of the unit matrix and Pauli matrices, see my comments here at the bottom). Classically, the arrangement of the square is impossible because the total number of red cards in the 9 drawers is even or odd if we count them by adding up rows or columns, respectively.

In quantum mechanics, there exists an initial state for which the total number may be even if counted by combining the rows, or odd if counting by combining the columns. That's possible because the individual qubits describing the \(3\times 3 = 9\) don't commute with each other – general enough observables in quantum mechanics almost never commute with each other. In fact, the \(3\times 3=9\) quantum bit (two possible eigenvalues of each, with a split of the Hilbert space to 50-50 percent) observables may be defined out of the two spins in such a way that the parity counted from the rows is the opposite than the parity counted from the columns for any state of the two electrons' spins! (One must emphasize that the nine qubits discussed here are not independent in the sense of pairwise-commuting and allowing all 512 combinations of eigenvalues. Instead, they are really nine different bit-like variables one may find on a 2-qubit, four-dimensional Hilbert space.)

If you consider quantum mechanics "weird", this experiment is at least as weird as the experiment discussed in Bell's theorem – and maybe it's weirder and sharper (even though Bell, Bohm, and similar "gurus" of the anti-quantum movement haven't contributed to that particular setup). But the essential reason that makes the classical intuition invalid is the same in both cases – and in virtually any other characteristic quantum mechanical experiment, too: Classical physics is simply wrong and the quantum measurements can never be thought of as unmasking a pre-existing objective feature of the reality in the classical sense. One may call this insight "contextuality" and some people do but it is the very same thing that Bohr, Heisenberg, Jordan, Born, Dirac, and others called "quantum mechanics". In particular, I am convinced that Bohr has coined the word "complementarity" for the exactly same feature of quantum mechanics and exactly the same reason why someone might use "contextuality" – they are exact synonyma. It's shameful if someone wants to claim credit just by promoting a new word.

Most of the people like the authors of this "magic contextuality" paper (but I am not sure whether these four people belong to the "majority") are honestly confused. They are just not getting quantum mechanics and they're running in circles all the time. They delude themselves with new words all the time and they never understand the physics of the old words correctly. With the new words, they always do something wrong again so they don't make any progress, either.

So while it is true that all observables (quantities that may be results of an actual doable experiment which implies, according to the general postulates of quantum mechanics, that they are always associated with linear Hermitian operators) are intrinsically contextual (this claim is really nothing else than Bohr's "complementarity" – and perhaps the same as the Heisenberg uncertainty principle and the added value by Bell and his followers is zero), the paper in Nature contains lots of patently wrong statements, too. A major example is the following sentence in the abstract:
Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality is already known to be a critical resource for achieving advantages with quantum communication.
This is complete bullšit, of course. "Non-locality" is in no way a kind of "contextuality" and there is absolutely no need for non-locality in quantum mechanics – and quantum field theory, string theory, and other (potential or real) Lorentz-invariant i.e. relativistic quantum theories are exactly local. The violation of one of the two features – locality or realism – is needed to understand the results of some quantum experiments. The general enough considerations show that it's the realism assumption that is wrong – while locality has to hold because of relativity.

The non-existence of realism in Nature implies that generic observables are contextual. Depending on the subtle definitions, "non-realist" and "contextual" (observables) may mean exactly the same thing. And indeed, the observables in Nature around us are both "non-realist" and "contextual". One may also define the adjectives for them to mean something else but this difference only matters if one focuses on stupid classical-like alternatives to quantum mechanics. In particular, with some definitions of the adjectives, the quantities postulated to "objectively exist" by the pilot wave theory are "realist" but "contextual". If you are focusing on actual physics, on correct theories that do naturally agree with the empirical data, you will realize that "non-realism" and "contextuality" are both true and pretty much equivalent features of the word around us.

I actually do believe that the paper contains some non-trivial stuff and the authors arguably know that my criticism is right on the money (although their bizarre comments about "non-locality" make me less certain) but the broader "weird" algorithm to sell this kind of work – including the potentially useful, new, and important work on quantum computation – to the broader public is just outrageous.

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