Can Wigner and his friend disagree on an ultimate measurement?

Question

My understanding, roughly, is that the Wigner's Friend thought experiment involves a situation in which there are two isolated apparatuses that act on entangled particles (for example, polarized photons), where one takes a measurement of the unknown state (e.g., the polarity) and the other checks for a diffraction pattern indicating whether or not a measurement has been taken on the entangled system. The apparent paradox comes from the fact that they can "disagree": it is possible to have a situation in which a measurement of the polarization has been made by one of the detection systems (call it detector "A"), but the other (detector "B") still sees a superposition.

My question is: if detector B then proceeds to observe the polarization of the light, can it disagree with the observation made by detector A? Or is the extent of their "disagreement" limited only to whether an observation has been made or not?

I have a vague sense that the premise of this question is confused - like, I think that diffraction pattern associated with observing a superposition is a statistical effect that only becomes visible over the course of many events, and so how would that distribution of polarizations be meaningfully compared in a way that yields any real information to the observations by detector A if the outcome is binomial? - but lacking the language to phrase the question precisely, I hope the intuition in question above is clear enough.

Answer 1

You appear to be describing a Bell test, which is an actual experiment, not Wigner's friend which is a variant on Schrodinger's cat.

In the Bell test, neither Alice nor Bob see a superposition. They see measurement results. There is no disagreement. Alice's observation does not make a change to Bob's observable results. Only afterwards, when the results are brought together, a correlation between their results is found, showing that there can be no explanation in classical mechanics for the correlation.

Wigner's friend performs a quantum experiment in a laboratory. He describes the result of his measurement. Wigner is outside the Laboratory and does not know the result. He described his friend as a wave function. They disagree on the description, because they have different information. This is used to illustrate that the structure of quantum mechanics concerns the information we have about nature, not the underlying structure of matter.