Why is Quantum Field Theory Local?

[atyy]

Regarding (b), all GPTs allow updating but by "Bayesian" we mean there is a unique way to update in late of data. In GPTs going beyond the Tsirelson bound $2\sqrt{2}$ there is an element of arbitrary choice in how one updates in light of data. This is what leads to a recent phrase: it's the most general GPT where one can still learn.

Could you give some references?

 

[Kolmo]

Could you give some references?

(b) is a corollary of (a) so it is simpler to see the proof of (a) first.

It's here:
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.032120

Freely available here:
https://arxiv.org/abs/1801.06347

 

[Kolmo]

Could you give some references?

To be more explicit there is also also a third condition proved to be equivalent in this paper, so the full list is that the theory is obeys the following which are all equivalent:

(a) The most general theory satisfying the Exclusion principle. Namely that if each of the pairs from a set of observables $A,B,C$ are compatible/co-measurable, then the whole set is co-measurable

(b) The most general one that permits Bayesian updating.

(c) The most general one which assigns probabilities to any repeatable ideal measurements.

(a) was originally a conjecture of Ernst Specker. Cabello proved (c) implies (a) and from there proves (a) in the paper I linked. After that he later proved (b) in (PDF free access):
https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.042001.