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An unknown quantum state of a single system cannot be discovered, as ameasured system is reprepare: it jumps into an eigenstate of the measuredobservable. This impossibility of finding the quantum state and other symptomsusually blamed on wave-packet collapse follow (as was recently demonstrated forpure states of measured systems) from unitarity (which does not, however, allowfor a literal collapse) and from the repeatability of measurements: Continuousunitary evolution and repeatability suffice to establish the discreteness thatunderlies quantum jumps. Here we consider mixed states of a macroscopic, opensystem (such as an apparatus), and we allow its microscopic state to changewhen, e.g., measured by an observer, provided that its salient features remainunchanged and that observers regard macroscopic state of the pointer asrepresenting the same record. We conclude that repeatably accessible states ofmacroscopic systems (such as the states of the apparatus pointer) mustcorrespond to orthogonal subspaces in the Hilbert space. The symmetry breakingwe exhibit defies the egalitarian quantum superposition principle and unitarysymmetry of the Hilbert space, as it singles out preferred subspaces. Weconclude that the resulting discreteness (which underlies quantum jumps)emerges from the continuity of the core quantum postulates plus repeatabilityalso in macroscopic and open, but ultimately quantum systems such as measuringdevices accessed by observers, where (in contrast with pure states ofmicrosystems) repeatability is paramount.

Wave-packet collapse and the core quantum postulates: Discreteness of quantum jumps from unitarity, repeatability, and actionable information