The interpretation of the concept of reduced state is a subtle issue that has
relevant consequences when the task is the interpretation of quantum mechanics
itself. The aim of this paper is to argue that reduced states are not the
quantum states of subsystems in the same sense as quantum states are states of
the whole composite system. After clearly stating the problem, our argument is
developed in three stages. First, we consider the phenomenon of
environment-induced decoherence as an example of the case in which the
subsystems interact with each other; we show that decoherence does not solve
the measurement problem precisely because the reduced state of the measuring
apparatus is not its quantum state. Second, the non-interacting case is
illustrated in the context of no-collapse interpretations, in which we show
that certain well-known experimental results cannot be accounted for due to the
fact that the reduced states of the measured system and the measuring apparatus
are conceived as their quantum states. Finally, we prove that reduced states
are a kind of coarse-grained states, and for this reason they cancel the
correlations of the subsystem with other subsystems with which it interacts or
is entangled.Comment: 26 page