  An unknown quantum state of a single system cannot be discovered, as a
measured system is reprepare: it jumps into an eigenstate of the measured
observable. This impossibility of finding the quantum state and other symptoms
usually blamed on wave-packet collapse follow (as was recently demonstrated for
pure states of measured systems) from unitarity (which does not, however, allow
for a literal collapse) and from the repeatability of measurements: Continuous
unitary evolution and repeatability suffice to establish the discreteness that
underlies quantum jumps. Here we consider mixed states of a macroscopic, open
system (such as an apparatus), and we allow its microscopic state to change
when, e.g., measured by an observer, provided that its salient features remain
unchanged and that observers regard macroscopic state of the pointer as
representing the same record. We conclude that repeatably accessible states of
macroscopic systems (such as the states of the apparatus pointer) must
correspond to orthogonal subspaces in the Hilbert space. The symmetry breaking
we exhibit defies the egalitarian quantum superposition principle and unitary
symmetry of the Hilbert space, as it singles out preferred subspaces. We
conclude that the resulting discreteness (which underlies quantum jumps)
emerges from the continuity of the core quantum postulates plus repeatability
also in macroscopic and open, but ultimately quantum systems such as measuring
devices accessed by observers, where (in contrast with pure states of
microsystems) repeatability is paramount.
