[kgwgk]

QBism has a cool name, but I think it's not as revolutionary as it may seem at first sight.

There are two kinds of uncertainty about a quantum system: the "classical" ignorance about what is the true quantum state and the non-determinism of the outcome of measurements even if the quantum state is perfectly known (note that only in this case the system can be described using a wave function).

"Up to an overall unitary ‘readjustment’ of one’s final probabilistic beliefs [...] quantum collapse is precisely Bayesian conditionalization."

I'd say that this 'readjustment' is the collapse with another name.

"Quantum measurement is nothing more, and nothing less, than a refinement and a readjustment of one’s initial state of belief. [...] Let us look at two limiting cases of efficient measurements. In the first, we imagine an observer whose initial belief structure ρ = |ψ⟩⟨ψ| is a maximally sharp state of belief. By this account, no measurement whatsoever can refine it. [...] The only state change that can come about from a measurement must be purely of the mental-readjustment sort: We learn nothing new; we just change what we can predict as a consequence of the side effects of our experimental intervention. That is to say, there is a sense in which the measurement is solely disturbance."

Ok, so when you do a measurement on a pure state (i.e. when the knowledge about the quantum state is maximal and cannot be refined by Bayesian updating):

instead of the "wave function collapse" of “standard” QM (the wave function changes to the eigenstate corresponding to the outcome of the measurement)

you have a "mental-readjustment" (because as a side effect of the measurement now you describe the system using the same wave function as in standard QM).

What are the problems with the "wave function collapse" that are solved by calling it "mental readjustment"?

https://www.perimeterinstitute.ca/personal/cfuchs/Oviedo.pdf

[n4r9]

I think the first thing to say is that the mathematics of quantum theory is the same no matter what interpretation you adhere to (with a small caveat for things like gravity-induced collapse). So, yes, collapse is unavoidable as a mathematical operation which we apply when making predictions about future events.

Where interpretations differ is in the physical content they assign to mathematical objects and operations. In some interpretations the wave function is "really objectively out there", but in others the wave function is "just a good way to store my beliefs about the future".

If you adhere to the former case, then either collapse is merely apparent (ie. many-worlds) or it's a real mechanical thing that is going on in the outside world. If you adhere to the latter case then the collapse process is merely an act of updating beliefs.

Now, if collapse is a real physical process then you run into the measurement problem and "Wigner's friend" style problems. At what point does collapse occur and what induces it? Why is quantum evolution reversible right up until the point of collapse? Is there a combined wave function describing both the observer and the system, and does that wave function collapse? etc... In QBism these issues do not arise because it makes perfect classical sense for, say, an observer of an observer to have beliefs about what that other observer believes.

[kgwgk]

> In some interpretations the wave function is "really objectively out there", but in others the wave function is "just a good way to store my beliefs about the future".

Those “beliefs about the future” may or may not be correct. If you describe a system with a wave function you claim that you know the quantum state perfectly and there is no margin for error.

How do you think QBism helps in the following scenario?

We have spins prepared in some state, say |up>. We agree that the wave function |up> gives a complete description of the quantum states. That’s our shared belief, if you will.

While you are not looking, I do perform some operations and the corresponding mental readjustments change my beliefs: now I describe the spins with the wave function |down>. You keep your original beliefs.

Now we measure the spins along that axis. I predict a negative outcome with 100% probability, you predict a positive outcome with 100% probability. I get it right every time, you get it wrong every time.

If the |down> quantum state is not "really objectively out there", how do you explain these results?

[n4r9]

I imagine a QBist would say that when you performed your additional secret operations you gained more information and therefore you were able to develop more accurate beliefs.

Is your issue that a belief can be completely wrong, or rather that two people can hold diametrically opposing beliefs?

[kgwgk]

I quoted above Fuchs, the main proponent of QBism, saying that in that example "We learn nothing new; we just change what we can predict as a consequence of the side effects of our experimental intervention. That is to say, there is a sense in which the measurement is solely disturbance." So it is not about refining our knowledge of the physical state as it was, it is about changing the physical state and learning what the new state happens to be.

Different people can have different beliefs (different descriptions of the physical state) but not all the beliefs are equally valid. We can in principle check how well they fit with the (shared, objective) reality. In general this is possible only statistically (comparing realized frequencies with calculated probabilities) but in the example above it can be done from a single event: if something impossible according to your beliefs does happen, your beliefs were incompatible with reality and therefore untenable.

[n4r9]

I think I'm with you but I don't understand how this is a criticism of QBism (if that's indeed what it is). It's possible for one's beliefs to turn out to be completely wrong because of some secret actions which you were not aware of. This is just as true classically as in the quantum regime. I don't see that this requires more of an explanation than we've already given it.

[kgwgk]

This is not a criticism of QBism. It's an explanation of what QBism says, as far as I understand, and how (at least in this case) it's no different from the standard QM description: the system of interest is initially in a known quantum state described by one wave function, we perform a measurement, the quantum state is now the eigenstate corresponding to the outcome of the measurement and described by a different wave function. In standard quantum mechanics the change in the quantum state is called "collapse of the wave function", in QBism it may be called "mental readjustment" but I fail to see any substantial difference if that "mental readjustment" comes together with an actual physical change in the system ("the measurement is solely disturbance").

I just find that it's misleading to say that

> in neo-Copenhagen interpretations like QBism the apparent collapse is merely a reflection of an agent's belief update process.

or

> in some interpretations the wave function is "really objectively out there", but in others [presumably including QBism] the wave function is "just a good way to store my beliefs about the future".