Ah, quantum mechanics, what has the idiot done to you?
So, he basically claims that homeopathic treatment is, at least to some approximation, an entanglement of two possible states
1. The remedy is effective, the 'doctor' is helpful, and the patient gets better
2. The remedy is ineffective, the doctor is unhelpful, and the patient gets worse.
These three terms are separate basis states of the patient, doctor and remedy, meaning if we look at any of them individually, we'd see they each have two states. As per basic QM, a total state is a combination of each of these (you can imagine them like vector components if you don't know QM).
This is a "maximally entangled state", or to be correct, the probability of either of these total states is 0.5. While not corresponding to reality, at least the math is not wrong.
Then we get to equation 4. He concludes that a double-blind study eliminates the effect of the doctor, so the doctor's helpful and unhelpful state becomes zero. This is wrong. We can either ignore the doctor, literally erasing his state from the equation, so we have
1. The remedy is effective, and the patient gets better
2. The remedy is ineffective, and the patient gets worse.
or we leave the doctor in a 50/50 split between being helpful and not helpful. The doctor can't be zero, he has to be something. A wavefunction of zero isn't normalizable, meaning it's not a possible state. It would be literally impossible to do a double blind study, like an electron going to an energy level lower than the ground energy.
However, in this state, there is an equal probability of the patient improving or not, so he is correct that on average, we should expect no result. Of course, he's forgets that this is an average, so each patient either gets better or worse, and they are measured individually. Really, his equation is says that double-blind studies are helpful by removing the effect of the doctor.
Of course, he makes other errors. For example, he assumes his "assessment operator" (capital Pi) produces even results. For example, if the patient |P> gets better, the assessment gives
<P+|PI|P+> = +health
or if the patient gets worse
<P-|PI|P-> = -health
so that for an even split between P+ and P-
<P+/-|PI|P+/-> = 0
Which he doesn't state, has no reason to conclude, and as anyone who has ever thought about medicine realizes, is so completely stupid it's a wonder he can put on his pants in one try.
The rest follows in a similar manner, alternating between copying from an undergrad QM textbook and replacing the variables, and using the physics so poorly it's not even wrong.