This question is about quantum reconstruction. I am new to this topic, and I decided to read some papers on it.
I selected some works which follow an "information-focused" approach. The authors of these works try to formulate QM through an alternate set of axioms, which avoids the standard quantum state-space structure (in terms of Hermitian operators/linear spaces) and is centered on the idea that the physical state can carry only a limited amount of information.
Some of these authors, after stating the postulates of the theory, use the standard QM formalism to get their results. This can be done because their “central” postulate about information includes some extra hypothesis about the linearity of the state space. Perhaps in some authors this extra hypothesis is somehow hidden, for example in  and , see below (but this is just my opinion).
Of course, since their works are on the reconstruction of QM, their aim is to obtain the same properties of standard QM, and linearity is among these properties.
My questions are:
1) When I say that linearity is somehow hidden, is my interpretation right?
2) Are there other theoretical works on quantum reconstruction which follow this idea of “limited information” systems but avoid any hypothesis about linearity? (but, anyway linearity will be a consequence of the axioms of that theories)
Here are some references:
 Caslav Brukner and Anton Zeilinger: http://quantmag.ppole.ru/Articles/Quo_Vadis_Quantum_Mechanics.pdf#page=60
 "Relational quantum mechanics" https://arxiv.org/abs/quant-ph/9609002
Borivoje Dakic and Caslav Brukner:
 Quantum theory and beyond: Is entanglement special? https://arxiv.org/abs/0911.0695
Even in Hardy's most cited work ( https://arxiv.org/abs/quant-ph/0101012), which doesn't follow an information-focused approach, there is a very strong "Simplicity" axiom which involves mathematical properties of the state space, closely related to linearity and Hilbert structure.