Lucien Hardy wrote a paper[1] showing how one "naturally" ends up with a quantum theory by demanding a few reasonable axioms. The paper also goes into how this implies complex numbers (and rules out quaternions).

Scott Aaronson has a more accessible (and humorous) article on it here[2].

Entanglement has been shown to be intimately linked to this[3] result, which is interesting given the experimental evidence[4] for entanglement.

Not my field, but I found this interesting at least.

[1]: https://arxiv.org/abs/quant-ph/0101012

[2]: https://www.scottaaronson.com/democritus/lec9.html

[3]: https://arxiv.org/abs/0911.0695

[4]: https://en.wikipedia.org/wiki/Quantum_entanglement#Notable_e...