Here is an interesting article by Dominik Janzing and Thomas Beth, both from Karlsruhe, Germany. The jist of the article is that if the world were more quantum, doctors would have to learn Bell inequalities!
On the potential influence of quantum noise on measuring effectiveness in clinical trials
ABSTRACT:To test the effectiveness of a drug, the medical researcher can instruct two randomly selected groups of patients to take the drug or not to take it. Each group should comply with the instructions exactly or else the causal effect cannot be identified satisfactorily. This holds true even when those who do not comply are identified afterwards, since latent factors such as patient’s personality can influence both his decision and his physical response. However, one can still give bounds on the effectiveness of the drug depending on the rate of compliance. They are described by 16 inequalities. Remarkably, the proofs for these bounds given in the literature rely on models that represent all relevant latent factors influencing patient’s behavior by hidden classical variables. In a strong analogy to the violation of Bell’s inequality, half of the inequalities fail if patient behavior is influenced by latent quantum processes (e.g. in his nervous system). Quantum effects could fake an increase in the recovery rate by about 13%, although the drug would hurt as many patients as it would help if everyone took it. We show that the other eight inequalities remain true even in the quantum case. We do not present a realistic model showing the above effect. We only point out that the physics of decision-making could be relevant for the causal interpretation of every-day life statistical data. Our derivation of the remaining eight inequalities suggests how to avoid problematic hidden-variable models in classical causal reasoning by representing all latent factors by quantum systems.
I’m guessing that this won’t help in the battle physicist’s have when teaching premed students (“Ooooh, but please just give me one more point on this quiz. Pleeeease!”)
The article is also on the arxiv under a slightly different title: Quantum noise influencing human behaviour could fake effectiveness of drugs in clinical trials. I have not been able to get a copy of the article as published in the International Journal of Quantum Information (cited above in your post), so I do not know if there are other differences.
I am pleased that you found this article. You wrote “…that if the world were more quantum, doctors would have to learn Bell inequalities!”
Maybe we should have emphasized that the effect described in our paper does not require any entanglement inside our body or our brain. Quantum coherence of one microscopic system (at least with 4-dimensional Hilbert space) is in principle sufficient. As long as we have no model of the brain and consciousness we cannot take for granted that there will be a hidden-variable model of the latter. I have no idea to what extent quantum effects play a role in our brain…
For me, it is not even clear how to define “quantum effects” in this context. Would we expect that all density matrices that appear at any time in our brain commute? Would we expect that all macroscopic effects triggered by our brain refer to a set of mutually commuting observables? Since a density matrix can never commute with all its time evolved matrices (unless the dynamics is trivial)the question is how much they should be non-commuting to call the system “quantum”.
The IJQI article “On the potential…” is online. It is the restructured and rewritten version of the quant-ph-paper “Quantum noise…”, but the statements are exactly the same. The IJQJ paper should be more readable.