Nothing in the underlying article seems truly quantum in the sense that there are quantum physical principles contributing to the outcomes of the experiments. Instead, authors used quantum probabilistic-inspired mathematics to analyze their results. In that, there isn't really anything truly interesting; that's just data modelling (and quantum math is structured to make modelling easier).
Certainly there are no claims of quantum physics being relevant. That would make me much more suspicious.
There's been a lot of "normal" bayesian modeling in cognitive psych and it has problems with the examples they address. So the point isn't data modeling per se, it is better data modeling, which is often worth a look.
Actually, if you read all the author's papers, they are strongly hinting at the underlying mechanism being quantum. But they never come quite out and say that.
Quantum mechanics does not permit parallel states to "communicate" in any way. The theory is purely linear (i.e. acts somewhat independently on all states), except for the wavefunction collapse phenomena. Any non-linenarity would, for instance, immediately imply that we can easily solve NP-complete problems using quantum computing:
So QM is probably a poor model for explaining human indecisiveness and irrationality. Much better is that it is simply the thing that evolution has come up with that can a) fit in our brains and b) yields proper results.
As far as I can see the question being addressed is which models best explain experimental results (at equivalent model complexity). If quantum(-like) probabilities pay off let's use them.
Up to now the models have mostly been a heap of heuristics but those produce models with lots of degrees of freedom that don't generalize well.
FWIW, the quantum nature of reality is harnessed by biological processes (see photosynthesis, for example[0]), and our attempts at modeling brains using classical computers have been remarkably inefficient, so far (compare the energy required by the server farm that simulates a mouse brain vs your metabolism).
I wouldn't be surprised if it turned out that cognition relied on quantum phenomena as well.
A good introduction might be this heavily cited paper from 2011 by another author, Busemeyer: "A quantum theoretical explanation for probability judgment errors"
He goes through the application of quantum probability, contrasts it with Komolgorov probability theory, and then walks through quite a few "anomalies" in cognitive psychology laying out specific models to deal with them.
The exposition of quantum vs. Komolgorov probability is clear and does not rely on specialized prior knowledge. The list of anomalies makes apparent the need for better modeling tools.
This sounds less like the mathematics behind quantum mechanics (eg: negative amplitudes) are themselves relevant, and more like quantum mechanics "bakes in" the kind of resource-bounded processing and causal structure that we expect good theories of cognition to have.
Last I've heard, probabilistic modelling of cognition - with resource-bounded processing and causal modelling in place of "pure" probability theory - has been a fairly successful research program. What advantage does quantum "complex" probability have over that, or over some generalizing to a measure theory with an arbitrary norm?
That mostly doesn't help, due to the fact that, as I understand the term, standard "decision theories" are intended as normative theories, meaning that when real behavior deviates, the investigators write the behavior off as wrong for failing to conform to theory, instead of trying to come up with a theory that actually describes the behavior.
So if you end up comparing an even-loosely-descriptive theory to a normative one, the descriptive theory will win, every time, no matter how far it is from true accuracy. That is, if you line up prospect theory, standard normative decision theory, and some new descriptive theory, the latter will definitely win in a model selection. But that doesn't tell us how the quantum descriptive theory compares to, for instance, the causal-probabilistic descriptive theory.
I don't understand your point in comparing this work to normative decision theories. The work is explicitly modeling experimental results that have been hard to model with existing probabilistic approaches.
That said, if we find that cognition can be well described by some fairly clean math, we should take a hard look at "normative" models that say it should be different. Up to now the descriptions have mostly had to use a pile of heuristics that could be (handwavingly) justified as "cheaper". But this work suggests a very different picture.
First, there's no strong evidence that biological brains make use of quantum phenomena except insofar as those phenomena drive normal chemistry.
Second, if brains do make use of quantum phenomena in weird ways, the effect would not be visible at a level as abstract as decision making. Such processes operate at the level of hundreds of millions of neurons, at which point classical approximations are quite accurate. Any strange quantum phenomenon would operate at the level of single neurons, outside of which the quantum numbers grow so large as to approach classical statistics.
This quantum mysticism needs to stop. There are much better ways to explain psychological effects like indecision than a (horrifically tenuous) analogy to quantum physics.
You are pattern matching very loosely. None of the work suggests any quantum phenomena affecting behavior. The papers go out of their way to reject that idea in detail.
The article says Wang "emphasized that her research program neither assumes nor proposes that our brains are literally quantum computers. Other research groups are working on that idea; Wang and her collaborators are not focusing on the physical aspects of the brain, but rather on how abstract mathematical principles of quantum theory can shed light on human cognition and behaviors."
