  The foundational studies of the standard, unitary-only quantum theory revolve
around the kinematical aspects of quantum entanglement and the improper quantum
mixtures. In this paper, we introduce and argue for the foundational character
of the question of dynamics of quantum subsystems (open quantum systems). In
this context, for some typical and physically relevant Markovian processes, we
technically prove non-existence of trajectories in the Hilbert state space of
the open system. As a kind of no-go theorem for the unitary-only quantum
theory, this finding suggests that the mixed quantum states may be joined to
the individual (single) quantum subsystem dynamically described by the
corresponding master equation. Then the problem of interpretation of improper
mixtures dissolves while description of quantum measurement boils down to the
problem of reduction of the mixed to the pure states-i.e. to the problem of
actualization of definite values of certain observables of the single open
systems, thus tackling the mathematical problem of interpreting probability for
the single trials of an experiment. This kind of indeterminism may be the
furthest we can go within the dynamical approach to quantum subsystems. As an
alternative appears the possibility that the idea of dynamics of quantum
subsystems may not be viable in the context of the unitary-only theory. As a
direct consequence of our main finding appears the a priori impossibility to
define "quantum history" in the Hilbert state space for the considered
Markovian models.
