  We introduce a protocol to transfer excitations between two noninteracting
qubits via purely dissipative processes (i.e., in the Lindblad master equation
there is no coherent interaction between the qubits). The fundamental
ingredients are the presence of collective (i.e. nonlocal) dissipation and
unbalanced local dissipation rates (the qubits dissipate at different rates).
The resulting quantum trajectories show that the measurement backaction changes
the system wave function and induces a passage of the excitation from one qubit
to the other. While similar phenomena have been witnessed for a non-Markovian
environment, here the dissipative quantum state transfer is induced by an
update of the observer knowledge of the wave function in the presence of a
Markovian (memoryless) environment -- this is a single quantum trajectory
effect. Beyond single quantum trajectories and postselection, such an effect
can be observed by histogramming the quantum jumps along several realizations
at different times. By investigating the effect of the temperature in the
presence of unbalanced local dissipation, we demonstrate that, if appropriately
switched on and off, the collective dissipator can act as a Maxwell's demon.
These effects are a generalized measure equivalent to the standard projective
measure description of quantum teleportation and Maxwell's demon. They can be
witnessed in state-of-the-art setups given the extreme experimental control in,
e.g., superconducting qubits or Rydberg atoms.
