Most derivations of the Born rule assume - among many other things - that measurements are somehow related to orthonormal bases. This is essentially equivalent to assuming that measurements correspond to self-adjoint operators. However, given Gleason's theorem, it should not come as a surprise that this brings us already close to the Born rule, and there is arguably no a priori reason whatsoever to begin with this assumption. Improving upon our earlier results of [1], I will present a derivation of the Born rule which does not make this assumption. In doing so, I will also point out some structural pitfalls that some philosophy colleagues have fallen into -- for example, modifying the Born rule implies that the partial trace loses its validity as the rule to compute local reduced quantum states.

[1] Ll. Masanes, T. D. Galley, and M. P. Müller, The measurement postulates of quantum mechanics are operationally redundant, Nature Communications 10, 1361 (2019).