To begin with, one should distinguish between “local” contextuality and “remote” contextuality. I have no problem with local contextuality. It simply means that the result of a measurement can reasonably depend on the disposition of the measuring apparatus, such as the orientation of the Stern-Gerlach apparatus. There is nothing nonclassical about that. Even in classical physics results of some measurements depend on the disposition of the measuring device. For example, the result of a coin toss experiment would depend on whether the tossed coin is collected in a bucket full of air or water, where air and water would represent two different contexts.

The “remote” contextuality, on the other hand, simply means nonlocality. The result Alice observes should not depend on the disposition or orientation of Bob’s measuring apparatus. If it does, then we have nonlocality. The 3-sphere model shows that there is no such thing as remote contextuality.

What is more, the earlier 3-sphere model without limiting processes is not even locally contextual, as we can clearly see from the definitions of the measurement functions in equations (16) and (17) in the paper you mention. The value of the results does not depend on the direction of measurements, a or a’.

There is also an algebraic notion of contextuality, which is related to the experimental contextuality I mentioned above. Alice’s choice of measurement direction can be either a or a’. But the local bivectors I.a and I.a’, or Pauli operators sigma.a and sigma.a’, do not commute. Therefore, one can say that the entire set of commuting operators defines one and the same context. This is a rather sophisticated notion that is preferred by mathematically inclined people who work on operator algebras, etc.

20th June is not a good time for me to attend the conference in Munich. But if you attend and see Chantal there, then please give her my regards.

Now qubits are the fundamental units of quantum information. Unlike classical bits, qubits can exist in a superposition of states. Meaning, they can be in both 0 and 1 states simultaneously, until measured. So, qubits, and thus QC, presume that quantum superposition is a real thing and not just a theoretical fantasy. Even if superposition were a real thing, in the end, it has to be measured to obtain classical bits, without which it would be impossible to do any reliable computation with QC.

Mikail Dyakonov’s objections to QC are at this practical level. By contrast, my lack of interest in QC is at the fundamental level because I think that Bell’s theorem is false, and quantum superposition is just an illusion caused by a lack of information about the complete state built with hidden variables.

Keep looking into such publications and find their hidden assumptions. Sometimes it takes a long time to figure out their missteps and mistakes. For example, I have worked on the GHZ theorem before, reproducing (in 2009) all of the predictions of the 3- and 4-particle GHZ states within the 7-sphere framework. But only recently I discovered the mistake in the GHZ argument itself, which I have now published in the one-page comment paper I linked above.

In modeling correlations, it is worth remembering that not all correlations are as strong as those predicted by the singlet state. The 2\/2 strength of the correlations is the strongest possible strength of any correlations predicted by quantum states. This was proved by the late mathematician Boris Tsirel’son. Thus, the directionality and orientations of the 3-sphere are needed only for the correlations of strengths greater than the bounds of 2 on the CHSH quantity. For the rest, such as those involving the “time of flight” of photons or quantum dots, the ordinary R^3 model of the physical space would suffice. Moreover, for those correlations that are stronger than the bounds of 2 on the CHSH quantity, we have the general 7-sphere framework (published in my Royal Society papers). That framework, although more complicated than the 3-sphere model, accommodates a local-realistic understanding of all possible correlations predicted by any general quantum state.

It is also important to remember that the purpose of a hidden variable interpretation is not to replace quantum theory but to provide a local-realistic foundation to it, similar to how statistical mechanics provided a deeper foundation for thermodynamics without replacing it.