[myridium]

In QM, evolution is unitary. The Born Rule is an empirical observation that is adequately explained by the decoherence of a quantum system into entangled states of observer, environment, measurement apparatus and the system being measured.

E.g. the master equation for a quantum density matrix governs its evolution when the environmental conditions are not completely known or modelled. Classical ensembles or 'decohered' states occur as a consequence.

QM is formulated as a deterministic theory. When you try to model an open, interacting system without tracking its environment, you have to sacrifice determinism in that model, because you are failing to track all the information in the system. You settle for probabilistic quantities. Nothing quantum about it either-- same thing happens in classical mechanics. They call this "classical thermodynamics".

[bryan0]

there might be some non-trivial deterministic unitary description via decoherence, but it should not be surprising that many people think that QM is non-deterministic.