EN
A common objective for quantum control is to force a quantum
system, initially in an unknown state, into a particular target
subspace. We show that if the subspace is required to be a
decoherence-free subspace of dimension greater than 1, then
such control must be decoherent. That is, it will take almost
any pure state to a mixed state. We make no assumptions
about the control mechanism, but our result implies that for
this purpose coherent control offers no advantage, in principle,
over the obvious measurement-based feedback protocol.