[ummonk]

Surely they'd just use tools from regular information theory and Bayesian inference? Quantum theory is just one particular application of information theory, where uncertainty is directly controlled by physical processes rather than simply due to imperfect knowledge.

[blurbleblurble]

Quantum information comes from Von Neumann entropy, while classical information comes from Shannon entropy. Regardless of where the "source" of information/uncertainty comes from or how "physical" it is, they're related but distinctly different tools which can each be applied to both "physical" or "non-physical" systems at any scale.

"Quantum" is turning out to have very little to do with how tiny or physical stuff is, and much more to do with assumptions about how observations emerge from interaction.

> rather than simply due to imperfect knowledge

That's the key right there... Quantum probability and quantum models don't rely on the existence of "perfect knowledge" or "underlying" objective states. States themselves are intrinsically probabilistic and contextually embedded. Measurements/observations cannot be cleanly decoupled from the states being measured, and are modelled as projections from a high dimensional space of possibilities onto some lower dimensional subspace.

This kinda thing works really well for social/cognitive systems which are incredibly sensitive to measurement process. For example, when conducting polls or surveys, the ordering of the questions is well known to impact the outcome. It turns out that this can be very well modelled using tools from quantum theory, and it has been.

Check out this book and all the books/papers citing it for a window into this fascinating world

https://link.springer.com/book/10.1007/978-3-642-05101-2

[ummonk]

Linear algebra (both for vector spaces and Hilbert spaces) is not really specific to quantum physics. What's specific to quantum physics is complex valued spaces, as opposed to ordinary statistics which works with real valued states.

And Von Neumann entropy is Shannon entropy, as applied to quantum states.